A Phase II Trial of the Immunogenicity of a DNA Plasmid-Based Vaccine (STEMVAC) Encoding Th1 Selective Epitopes From Five Antigens Associated With Breast Cancer Stem Cells (MDM2, YB1, SOX2, CDH3, CD105) in Patients With Metastatic Triple-Negative Breast Cancer

Inclusion Criteria: * Patients must be at least ≥ 18 years of age * Note: Because no dosing or adverse event (AE) data are currently available on the use of STEMVAC in patients \< 18 years of age, children and adolescents are excluded from this study, but will be eligible for future pediatric trials, if applicable * Patients with Eastern Cooperative Oncology Group (ECOG) Performance Status Score of ≤ 2 * Histologically confirmed triple-negative breast cancer * Tumors with estrogen receptor (ER)-low (≤ 5%) or negative and progesterone receptor (PR)-low (≤ 5%) or negative will be included * HER2-negative or HER2-low will be defined by the American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) 2023 "Human Epidermal Growth Factor Receptor 2 (HER2) Breast Testing Guideline Update" which reaffirms the 2018 "HER2 Breast Testing Guideline Focused Update" * Tumor is negative for PD-L1 marker testing per standard of care immunohistochemistry 22C3 pharmDx assay * Metastatic disease that is measurable based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Target lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * Have at least 1 site of disease confirmed by the treating oncologist that could be biopsied during treatment. This site should not be a site that is used to determine measurable disease for efficacy purposes. Lesions that will be biopsied should not be in a previously irradiated area unless progression has been demonstrated in such lesions * Patients should not have received any prior cancer immunotherapy in the metastatic setting * Prior Food and Drug Administration (FDA)-approved antibody drug conjugates are allowed * Patients are appropriate candidates to receive standard of care chemotherapy as per treating oncologist's clinical judgement * Patients who have received prior neoadjuvant or adjuvant chemotherapy are allowed * A minimum of 14 days washout since last systemic therapy or any palliative radiotherapy is required * Treatment with a bisphosphate or denosumab concurrently with protocol-specific therapy is allowed while on study (it is not exclusionary) * Patients must be at least 28 days post systemic steroids prior to enrollment, unless this is a steroid administered concurrently with chemotherapy or used as part of prophylaxis to prevent intravenous (IV) contrast reactions * Must have recovered from major infections and/or surgical procedures; and in the opinion of the investigator, not have any significant active concurrent medical illnesses or condition precluding protocol treatment * Willing to undergo up to two serial biopsies while on study * White blood cell (WBC) ≥ 2500/mm\^3 (Within 28 days of receiving first study vaccine) * Lymphocyte count ≥ 500/mm\^3 (Within 28 days of receiving first study vaccine) * Absolute neutrophil count (ANC) ≥ 1000/μL (Within 28 days of receiving first study vaccine) * Hemoglobin (Hgb) ≥ 9 g/dL (Within 28 days of receiving first study vaccine) * Platelets ≥ 75,000/μL (Within 28 days of receiving first study vaccine) * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN), except patients with Gilbert's syndrome in whom total bilirubin must be \< 3.0 mg/dL (Within 28 days of receiving first study vaccine) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤ 1.5 x institutional ULN (Within 28 days of receiving first study vaccine) * Creatinine ≤ 1.5 x ULN mg/dL or creatinine clearance \> 60 mL/min (Within 28 days of receiving first study vaccine) * Patients of child-bearing potential must agree to use dual methods of contraception and have a negative urine pregnancy test at screening, and male patients must use an effective barrier method of contraception if sexually active with a person of child-bearing potential. Acceptable methods of contraception are abstinence, condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal. Effective methods of contraception must be used throughout the study until the end of treatment on study Exclusion Criteria: * Patient has received more than one line of prior therapy in metastatic setting * Patients with tumors that are PD-L1-positive per standard of care immunohistochemistry 22C3 pharmDx assay * Enrollment in a concurrent interventional clinical trial. Biomarker or tissue collection or any other non-interventional clinical trial enrollment is allowed * Patients with any of the following cardiac conditions: * Symptomatic restrictive cardiomyopathy * Dilated cardiomyopathy * Unstable angina within 4 months prior to enrollment * New York Heart Association functional class III-IV heart failure on active treatment * Symptomatic pericardial effusion * Patients with any autoimmune disease or comorbidities that require chronic systemic steroids or immunosuppressants. Patients with conditions requiring inhaled, intranasal or topical steroids are permitted * Known hypersensitivity reaction to the granulocyte-macrophage colony stimulating factor (GM-CSF) adjuvant; any known contra-indication to GM-CSF * A non-breast malignancy requiring radiation or systemic therapy within last 5 years or any B-cell malignancy (e.g., chronic lymphocytic leukemia or follicular lymphoma) under active surveillance * Pregnant and breastfeeding individuals * Known history of human immunodeficiency virus (HIV) infection, hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive), or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Major surgery within the 4 weeks prior to initiation of study vaccine * Must be 14 days between a non-study vaccine, including live attenuated and non-live vaccines and any STEMVAC vaccination * Note: The minimum of 14 days does not apply to the tetanus and diphtheria (Td) vaccine * Any condition that may interfere with the patient's participation in the study per treating physician