A Phase I/IIa Multi-center, Open-label Master Protocol Dose Escalation and Expansion Study of AZD8205 as Monotherapy and in Combination With Anticancer Agents in Participants With Advanced Solid Tumors (BLUESTAR)

Key Inclusion Criteria: * Age ≥ 18 years * Relapsed/metastatic solid tumors treated with prior adequate standard of care therapy for tumor type and stage of disease or where in the opinion of the Investigator, a clinical trial is the best option for the next treatment based on response and/or tolerability to prior therapy. * Measurable disease per RECIST v1.1 * Eastern Cooperative Oncology Group (ECOG) Performance Status: 0-1 * Life expectancy ≥ 12 weeks * Adequate bone marrow, hepatic, and renal function as defined in the protocol Additional Inclusion Criteria For Sub-Study 1 Part A: • Histologically or cytologically confirmed metastatic or locally advanced/recurrent breast cancer, ovarian cancer, BTC or endometrial cancer Additional Inclusion Criteria For Sub-Study 1 Part B: * Histologically or cytologically confirmed metastatic or locally advanced and recurrent disease for the respective cohort: 1. Cohort B1 (Biliary Tract Cancer) 2. Cohort B2 (Ovarian Cancer) 3. Cohort B3 (Breast Cancer) 4. Cohort B4 (Endometrial Cancer) 5. Cohort B5 (Squamous Non-Small Cell Lung Cancer) Additional Inclusion Criteria For Sub-Study 2 Part A: * Minimum body weight ≥ 30 kg. * Histologically or cytologically confirmed metastatic or locally advanced/recurrent breast cancer, ovarian cancer, BTC, endometrial cancer or squamous non-small cell lung cancer. Additional Inclusion Criteria For Sub-Study 3 Part A: * Minimum body weight ≥ 30 kg (for participants enrolled in cohorts including rilvegostomig only). * Histologically or cytologically confirmed metastatic or locally advanced/recurrent breast cancer, ovarian cancer, BTC, endometrial cancer or squamous non-small cell lung cancer. Additional Inclusion Criteria For Sub-Study 4 Part A: * Minimum body weight ≥ 30 kg (for participants enrolled in cohorts including rilvegostomig only). * Histologically or cytologically confirmed metastatic or locally advanced/recurrent breast cancer, endometrial cancer or squamous non-small cell lung cancer. * Participants must have progressed following at least one but no more than 3 prior lines of treatment for metastatic or relapsed disease and have no satisfactory alternative treatment option as judged by the Investigator. Key Exclusion Criteria: * Treatment with any of the following: 1. Nitrosourea or mitomycin C within 6 weeks prior to the first dose of study treatment 2. Any investigational agents or study drugs from a previous clinical study within 5 half-lives or 28 days (whichever is shorter) prior to the first dose of study treatment 3. Any other anticancer treatment within the following time periods prior to the first dose of study intervention: 1. Cytotoxic treatment: 21 days 2. Non-cytotoxic drugs: 21 days or 5 half-lives (whichever is shorter) 3. Biological products including immuno-oncology agents: 28 days * Spinal cord compression or a history of leptomeningeal carcinomatosis. * Brain metastases unless treated, asymptomatic, stable, and not requiring continuous corticosteroids at a dose of \> 10 mg prednisone/day or equivalent for at least 4 weeks prior to start of study. * Active infection including tuberculosis and HBV, HCV or HIV * History of (non-infectious) ILD/pneumonitis that required steroids, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. * Clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses * Participants with any of the following cardiac criteria: 1. History of arrhythmia which is symptomatic or requires treatment (NCI CTCAE v5.0 Grade 3); symptomatic or uncontrolled atrial fibrillation, or asymptomatic sustained ventricular tachycardia. 2. Uncontrolled hypertension. 3. Acute coronary syndrome/acute myocardial infarction, unstable angina pectoris, coronary intervention procedure with percutaneous coronary intervention, or coronary artery bypass grafting within 6 months. 4. History of brain perfusion problems (eg, carotid stenosis) or stroke, or transient ischemic attack in the last 6 months prior to screening. 5. Symptomatic heart failure (NYHA class ≥ 2). 6. Prior or current cardiomyopathy. 7. Severe valvular heart disease. 8. Mean resting QTcF \> 470 msec. 9. Risk factors for QTc prolongation or risk of arrhythmic events such as heart failure, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age. * Patients with history of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with features suggestive of MDS/AML (as determined by prior diagnostic investigation) Additional Exclusion Criteria For Sub-Study 2 Part A: * Thromboembolic event within 3 months before the first dose of study intervention - No longer applicable per amendment 7 * Experienced a toxicity that led to permanent discontinuation of prior immunotherapy. * Active or prior documented autoimmune or inflammatory disorders requiring chronic treatment with steroids or other immunosuppressive treatment. * History of organ transplant Additional Exclusion Criteria For Sub-Study 2 Part B • Previous treatment with any therapy that contains a TOP1i (eg. irinotecan, topotecan, trastuzumab deruxtecan, etc.) Additional Exclusion Criteria For Sub-Study 3 Part A: * Concomitant use of medications or herbal supplements known to be strong cytochrome P (CYP) 3A4 inducers/inhibitors. * Any history of persisting (\> 2 weeks) severe cytopenia due to any cause * Patients with any known predisposition to bleeding * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of saruparib. * Previous treatment with any therapy that contains a TOP1i (eg. irinotecan, topotecan, trastuzumab deruxtecan, etc.) Additional Exclusion Criteria For Sub-Study 4 Part A: * Patients have received prior therapy with AZD9574 or more than 1 prior line of any other PARPi-based regimen * Concomitant use of medications or herbal supplements known to be strong cytochrome P (CYP) 3A4 inducers/inhibitors. * Previous treatment with rilvegostomig for the cohort treated with rilvegostomig * Previous treatment with any therapy that contains a TOP1i (eg. irinotecan, topotecan, trastuzumab deruxtecan, etc.) * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of AZD9574