An Open-label, Dose Escalation and Expansion, Phase 1/2 Trial to Evaluate the Safety, Tolerability, Pharmacokinetics, Pharmacodynamics, and Efficacy of TAK- 188, an Anti-CCR8 Antibody-Drug- Conjugate, as a Single Agent in Adult Participants With Locally Advanced or Metastatic Solid Tumors

Inclusion Criteria: 1. Participants ≥18 years or ≥ the local legal age of majority, as applicable, at the time of signing the ICF. 2. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. 3. Participants must provide biopsy samples (core needle or other surgical procedure) collected within 28 days prior to C1D1 and also on treatment unless procedure is determined to be unsafe following discussion with sponsor. Participants with an archival biopsy specimen collected within 90 days prior to C1D1 of TAK-188 who have not received any other cancer-specific treatment (with the exception of adjuvant endocrine therapy for a history of breast cancer) at least 14 days prior to the biopsy and throughout the period leading up to C1D1 may use that archival specimen in lieu of a new pretreatment biopsy. Archival biopsy from the same tumor must be provided, if available. 4. Adequate bone marrow, renal, and hepatic functions, as determined by the following laboratory parameters: 1. Absolute neutrophil count (ANC) ≥1500 per microliter (μL), platelet count ≥75,000/μL, and hemoglobin (Hgb) ≥8.0 g/dL without growth factor support for ANC or transfusion support for platelets within 14 days before the first trial treatment dose. Transfusion of packed red blood cells is allowed, post infusion Hgb must be greater than 8.0 g/dL. 2. Total bilirubin ≤1.5 times the institutional upper limit of the normal range (ULN). For participants with Gilbert's disease, ≤3 milligrams per deciliter (mg/dL). 3. Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3.0 × ULN or baseline or ≤5.0 × ULN or baseline with liver metastases. 4. Albumin ≥3.0 grams per deciliter (g/dL). 5. Calculated creatinine clearance CLCR (using the Cockcroft-Gault formula) ≥60 mL/minute. 6. Left Ventricular Ejection Fraction (LVEF) \>50%, as measured by echocardiogram or multiple-gated acquisition scan (MUGA) within 4 weeks before receiving the first dose of TAK-188. 5. Clinically significant toxic effects of previous therapy have recovered to Grade 1 (per NCI CTCAE v5.0) or baseline, except for alopecia, Grade 2 peripheral neuropathy, and/or autoimmune endocrinopathies with stable endocrine replacement therapy. 6. Female participants must be: 1. Postmenopausal (natural amenorrhea and not due to other medical reasons) for at least 1 year before the screening visit, or 2. Surgically sterile, or 3. If they are of childbearing potential, agree to practice 2 effective methods of contraception at the same time, from the time of signing the informed consent through 180 days after the last dose of TAK-188, or 4. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant. 5. Periodic abstinence (for example, calendar ovulation, symptothermal, postovulation methods), withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. 7. Male participants, even if surgically sterilized (that is, status postvasectomy), must: 1. Agree to practice effective barrier contraception (that is, a condom) during the entire trial treatment period and through 180 days after the last dose of TAK-188, or 2. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant. 3. Periodic abstinence (for example, calendar ovulation, symptothermal, postovulation methods), withdrawal, and spermicides only are not acceptable methods of contraception. 8. Voluntary written consent must be given before performance of any trial-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care. 9. Participants with controlled Human Immunodeficiency Virus (HIV) are allowed: 1. Cluster of differentiation 4 (CD4) cell count greater than 350 cell per cubic millimeters (cell/mm\^3). 2. Viral load undetectable for at least a year. 10. The following solid tumor participants will be allowed: a. Participants with the following pathologically confirmed (cytological diagnosis is adequate) locally advanced or metastatic solid tumors, who have progressed on all standard, curative, or life-prolonging treatments (or are intolerant to all available standard therapies): i. Gastroesophageal (esophageal, gastroesophageal junction, and gastric) adenocarcinoma and squamous cell carcinoma. ii. PDAC. iii. Nonsquamous and squamous NSCLC (participants with actionable genomic alteration \[AGAs\] are allowed in dose escalation only). iv. squamous cell carcinoma of head and neck (SCCHN). v. Colorectal cancer. 11. Participants with metastatic or advanced solid tumors must have radiographically measurable disease per RECIST Version 1.1. Lesions to be used as measurable disease for the purpose of response assessment must either a) not reside in a field that has been subjected to prior radiotherapy or b) have demonstrated clear evidence of radiographic progression since the completion of prior radiotherapy and before trial enrollment or c) have been radiated at least 6 months before trial enrollment or d) should not be the same lesion selected for mandatory biopsy at screening. 12. For expansion in NSCLC (post programmed cell death-ligand 1 \[PD-L1\] treatment): 1. Participants with pathologically confirmed (cytological diagnosis is adequate) locally advanced or metastatic NSCLC. 2. Participants must have tested negative for a known AGA (for example, estimated glomerular filtration rate (EGFR), anaplastic lymphoma kinase (ALK), mesenchymal epithelial transition \[MET\], c-ros oncogene 1 \[ROS1\], BRAF). 3. Must have had disease progression in the advanced or metastatic setting. No more than 1 line of therapy in advanced or metastatic setting is permitted. 4. Participants must have received at least 6 weeks of 1 prior anti-PD-(L)1 therapy, and this must have been given during the immediately preceding line of therapy. Anti-PD-(L)1 therapy may have been given in the metastatic or neoadjuvant setting. 5. Participants are eligible regardless of PD-L1 status but this information must be provided. 6. NOTE: Prior anti-PD-(L)1 therapy may have been given with or without an anti-CTLA-4 antibody and/or chemotherapy (for example, carboplatin and pemetrexed). 13. For Phase 1 backfill and possible expansion, in SCCHN (post PD-(L)1 treatment): 1. Participants with histologically confirmed (cytological diagnosis is acceptable) metastatic or unresectable, recurrent SCCHN that is considered incurable by local therapies. Participants should have PD-(L)1 monotherapy or in combination with chemotherapy administered in the recurrent or metastatic setting or neo-adjuvant/adjuvant. Anti-PD-(L)1 therapy must have been given during the immediately preceding line of therapy. No more than 1 line of therapy in advanced or metastatic setting is permitted. 2. Anatomic subsites to be included are oral cavity, oropharynx, hypopharynx, larynx, nasal cavity, and paranasal sinuses (maxillary, ethmoid, sphenoid, and frontal). The exception to this is nasopharyngeal cancer and salivary gland tumors, which will not be included. 3. Participants with oropharyngeal cancer or tumors arising in the paranasal sinuses (maxillary, ethmoid, sphenoid, and frontal) must agree to provide archival tissue for human papillomavirus (HPV) testing or if known, HPV testing results using CINtec p16 histology assay and a 70% cutoff point must be provided. If HPV status was previously tested using this method, no additional testing is required. Otherwise, if another validated HPV assay was performed, tissue will be required for central confirmation. 4. Tumors must have a PD-L1 CPS ≥1. 14. For dose expansion in gastroesophageal adenocarcinoma (GEA) (post PD-(L)1 treatment): 1. Participants with pathologically confirmed (cytological diagnosis is adequate) locally advanced or metastatic gastroesophageal (esophageal, gastroesophageal junction, and gastric) adenocarcinoma. 2. Must have had disease progression while on or following 1 prior line of therapy: 3. Disease progression while on or following at least 6 weeks of 1 prior anti-PD-(L)1 therapy in the recurrent locally advanced or metastatic setting. Prior anti-PD-(L)1 therapy may have been given with or without chemotherapy (for example, mFOLFOX or CAPOX); CAPOX); HER-2 positive participants must have received trastuzumab. Anti-PD-(L)-1 therapy must have been given during the immediately preceding line of therapy. No more than 1 line of therapy in advanced or metastatic setting is permitted. 4. Tumors must have a PD-L1 CPS ≥1. Exclusion Criteria: 1. History of any of the following cardiac illnesses within 6 months before first dose of TAK-188: 1. Congestive heart failure New York Heart Association Grade III or IV. 2. Unstable angina, myocardial infarction. 3. Persistent hypertension ≥160/100 mm mercury (Hg) despite optimal medical therapy. 4. Ongoing cardiac arrhythmias of Grade \>2 (including atrial flutter/fibrillation or intermittent ventricular tachycardia). 5. Other ongoing serious cardiac conditions (for example, Grade 3 pericardial effusion or Grade 3 restrictive cardiomyopathy). 6. Symptomatic cerebrovascular events. 7. Chronic, stable atrial fibrillation on stable anticoagulation therapy, including low molecular-weight heparin, is allowed. 2. Baseline prolongation of Fridericia-corrected QT interval (QTcF) (for example, repeated demonstration of QTc \>480 milliseconds, history of congenital long QT syndrome, or torsades de pointes) on a 12-lead ECG during the screening period. If participants are taking medications known to prolong QTc at screening, participants may continue to take these medications as long as their baseline QTcF is \<480 milliseconds. Participants may not start using such medications on or after C1D1. 3. Oxygen saturation of \<90% of room air at screening. 4. Participants treated with other chemokine (C-C motif) receptor 8 (CCR8) targeting agents within the past 6 months. 5. Active diagnosis of lung conditions including: 1. Pneumonitis. 2. Interstitial lung disease. 3. Severe chronic obstructive pulmonary disease. 4. Idiopathic pulmonary fibrosis. 5. Other restrictive lung diseases. 6. Acute symptomatic pulmonary embolism. 7. Grade ≥2 pleural effusion not controlled by tap or requiring indwelling catheters. 6. History of known brain metastasis or leptomeningeal disease unless: 1. Brain metastases are stable on cranial imaging (that is, ≥4 weeks) following prior surgery, whole-brain radiation OR 2. Stereotactic radiosurgery and off corticosteroids for brain metastases 3. Must be without neurologic dysfunction that would confound the evaluation of neurologic and other AEs. 7. Grade ≥2 fever of malignant origin. 8. Systemic infection requiring IV antibiotic therapy or other serious infection within 14 days before the first dose of TAK-188 or severe infections on continued treatment. 9. Participants with uncontrolled, known or suspected, autoimmune disease. Participants with vitiligo, type I diabetes mellitus, residual hypothyroidism due to an autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. 10. Participants with a diagnosis of an identified congenital or acquired immunodeficiency (for example, common variable immunodeficiency, uncontrolled HIV infections, organ transplantation). 11. Chronic, active hepatitis (for example, participants with known hepatitis B surface antigen seropositive and/or detectable HCV RNA). Note: 1. Participants who have positive hepatitis B core antibody can be enrolled but must have an undetectable serum hepatitis B virus-DNA. 2. Participants who have positive HCV antibody must have an undetectable HCV-RNA serum level. 12. Prior or current clinically significant ascites, as measured by physical examination, that requires active paracentesis for control. 13. Any pre-existing medical or psychiatric condition or illness, metabolic dysfunction, physical examination finding, or clinical laboratory finding that gives reasonable suspicion of a disease or condition that would contraindicate the use of an investigational drug or that would limit compliance with trial requirements or compromise ability to provide written informed consent. Participants with a history of PE on anti-coagulation are permitted unless symptomatic requiring oxygen supplementation. 14. Recent major surgery where the participant has not fully recovered based on physician assessment. 15. Recent major bleeding event that has not resolved, and the underlying reason for bleeding has not been corrected. 16. Participant with concurrent malignancy requiring active treatment, with the exception of participants on chronic hormonal therapy. 17. Treatment with fully human/humanized antineoplastic monoclonal antibodies less than 4 weeks or the time period equal to the dosing interval, whichever is shorter. No washout period is required for prior treatment with anti-PD-(L)1 antibodies. 18. Treatment with any investigational products or other anticancer therapy (including chemotherapy, targeted agents, and immunotherapy), within 14 days or 5 half-lives, whichever is shorter, before C1D1 of TAK-188. 19. Concurrent chemotherapy, immunotherapy, biologic, or hormonal therapy (with the exception of adjuvant endocrine therapy for a history of breast cancer). Concurrent use of hormones for noncancer-related conditions is acceptable (except for corticosteroid hormones). 20. Radiation therapy within 14 days (42 days for radiation to the lungs) and/or systemic treatment with radionuclides within 42 days before C1D1 of TAK-188. Participants with clinically relevant ongoing pulmonary complications from prior radiation therapy are not eligible. 21. Use of systemic corticosteroids or other immunosuppressive therapy, concurrently or within 7 days of C1D1 of TAK-188, with the following exceptions: 1. Topical, intranasal, inhaled, ocular, intra-articular, and/or other nonsystemic corticosteroids. 2. Physiological doses of replacement steroid therapy (for example, for adrenal insufficiency). 3. Single doses of steroids (for example, for imaging premedication) within the 7-day timeframe may be allowed after clarification with sponsor. 22. Receipt of live attenuated vaccine (for example, tuberculosis Bacillus Calmette-Guerin vaccine, oral polio vaccine, measles, rotavirus, yellow fever) within 28 days of C1D1 of TAK-188. Non-live, approved vaccines are allowed (for example, COVID-19 vaccine). a. Note: COVID-19 vaccination should not be given within ±3 days of systemic trial treatments. 23. Recipients of stem cell transplantation or organ transplantation. 24. Female participants who are lactating or have a positive serum/urine pregnancy test during the screening period or a positive serum/urine pregnancy test on Day 1 before first dose of TAK-188. a. Note: Female participants who are lactating will be eligible if they choose to discontinue breastfeeding before the first dose of TAK-188. 25. Participant is a trial site employee, a site employee's immediate family member (for example, spouse, parent, child, sibling), or is in a dependent relationship with a site employee who is involved in conduct of this trial or may consent under duress. 26. Participant is considered to be vulnerable, as defined per local regulations and if exclusion is required by local regulations. Examples are persons under safeguard of justice, persons deprived of liberty by judicial or administrative decision, persons receiving psychiatric care without their consent, persons admitted to a health or social establishment for purposes other than research, persons of full age who are subject to a legal protection measure (guardianship or curatorship), and persons unable to express their consent.