Inclusion Criteria:
* Able to understand and give written informed consent.
* Assigned female or male at birth, 18 years of age or older.
* Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1.
* Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 criteria by investigator assessment.
* Organ function requirements:
* Adequate hematologic function
* Adequate hepatic function
* Creatinine clearance
* Coagulation
* Tissue requirement:
* Parts A, B, C, and D:
* Pre-treatment tumor tissue is required.
* Parts A and C backfill biopsy cohorts:
* Participants must agree to fresh pre- and on-treatment biopsies.
* Participants assigned male at birth and participants assigned female at birth and of childbearing potential who engage in heterosexual intercourse must agree to use protocol-specified method(s) of contraception
* Willing and able to comply with the requirements and restrictions in this protocol
* Part A (GS-0201 Monotherapy Dose Escalation) Inclusion Criteria:
* Histologically/cytologically confirmed progressive/advanced solid tumors with selected molecular lesions.
* Participants must have received, been intolerant to, or been ineligible for all treatment known to confer clinical benefit or have a contraindication to receive the therapy
* Part B (Dose Expansion) Inclusion Criteria:
* Disease documented as:
* Cohort B1:
* Histologically or cytologically confirmed progressive/advanced selected solid tumor diagnoses harboring defined molecular lesions
* Participants may potentially be required to forgo treatment with approved agent(s) to be able to participate in the study
* Cohort B2:
* Histologically or cytologically confirmed progressive/advanced solid tumor diagnoses harboring defined molecular lesions not included in Cohort B1
* Participants must have received, been intolerant to, or been ineligible for all treatment known to confer clinical benefit or have a contraindication to receive the therapy
* Part C (Dose Escalation) Inclusion Criteria:
* Histologically or cytologically confirmed unresectable locally advanced/metastatic selected solid tumors
* Part D (Dose Expansion) Inclusion Criteria:
* Disease documented as:
* Cohort D1:
* Histologically or cytologically confirmed unresectable locally advanced or metastatic triple-negative breast cancer (mTNBC)
* Cohort D2:
* Histologically or cytologically confirmed unresectable locally advanced or metastatic HR+/HER2- (IHC 0, IHC 1+ or IHC 2+/ in situ hybridization (ISH-)) breast cancer.
Exclusion Criteria:
* Pregnant or lactating females
* Known hypersensitivity to any of the study drugs, its metabolites, or formulation excipients
* Requirement for ongoing therapy with or use of any prohibited medications described in the protocol
* Participants with myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with findings suggestive of MDS/AML
* Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of GS-0201
* The therapies listed below within the specified timeframe:
* Major surgery (excluding minor procedures, eg, placement of vascular access, gastrointestinal/biliary stent, biopsy) \< 4 weeks prior to planned Cycle 1 Day 1
* Immunotherapy or biologic therapy \< 21 days prior to planned Cycle 1 Day 1
* Chemotherapy \< 14 days prior to planned Cycle 1 Day 1, or \< 42 days for mitomycin or nitrosoureas
* Targeted small molecule therapy \< 14 days prior to planned Cycle 1 Day 1
* Receipt of experimental therapy within 21 days or 5 experimental treatment half-lives (whichever is longer) prior to planned Cycle 1 Day 1
* Hormonal or other adjunctive therapy for cancers other than the cancer under evaluation in this study that started \< 14 days prior to planned Cycle 1 Day 1 are not permitted. Hormonal therapy, bisphosphonates, somatostatin analogues, and leuprolide are permitted if started ≥ 14 days prior to planned Cycle 1 Day 1
* Radiotherapy within 2 weeks prior to planned Cycle 1 Day 1 and the radiation is not administered to a target lesion
* Any prior allogeneic tissue/solid organ transplantation, including allogeneic hematopoietic stem cell transplantation. Participants with a history of autologous hematopoietic stem cell transplantation are also excluded
* Have not recovered (ie, Grade 1 or lower) from AEs due to a previously administered agent
* Prior treatment with approved or experimental prohibited agents as detailed in the protocol.
* Diagnosis of immunodeficiency, either primary or acquired, or requires systemic corticosteroids (\> 10 mg of prednisone daily, or equivalent). However, replacement doses, topical, ophthalmologic, and inhalational steroids are permitted
* Have an active second malignancy
* Have known active central nervous system (CNS) metastases
* Participants with carcinomatous meningitis or primary CNS tumors are excluded regardless of clinical stability
* Meet any of the following criteria for cardiac disease:
* Myocardial infarction or unstable angina pectoris within 6 months of enrollment
* History of serious ventricular arrhythmia (ie, ventricular tachycardia or ventricular fibrillation), high-grade atrioventricular block, or other cardiac arrhythmias requiring antiarrhythmic medications (except for atrial fibrillation that is well controlled with antiarrhythmic medication)
* QT interval \> 470 msec
* New York Heart Association Class III or greater congestive heart failure or known left ventricular ejection fraction less than 40%
* Meet any of the following infectious criteria:
* Have active serious infection requiring antimicrobials
* Have active hepatitis B virus (HBV) or hepatitis C virus (HCV), or HIV. In participants with a history of HBV or HCV, participants with detectable viral loads will be excluded
* Participants who test positive for hepatitis B surface antigen. Participants who test positive for hepatitis B core antibody are eligible with a negative HBV DNA by quantitative Polymerase chain reaction (PCR)
* Participants who test positive for HCV antibody. Participants who test positive for HCV antibody are eligible with a negative HCV RNA by quantitative PCR
* Participants who test positive for HIV antibody
* History of pneumonitis requiring treatment with corticosteroids, interstitial lung disease, or radiation pneumonitis requiring steroids
* Symptomatic ascites or pleural effusion
* Have other concurrent medical or psychiatric conditions that, in the investigator's opinion, may be likely to confound study interpretation or prevent completion of study procedures and follow-up examinations
* Any medical condition that, in the investigator's or sponsor's opinion, poses an undue risk to the participant's participation in the study
* Use of any live vaccines against infectious diseases within 4 weeks (28 days) of initiation of study drug(s) (inactivated, viral vector vaccines, and messenger RNA (mRNA) vaccines are allowed; seasonal vaccines should be up to date prior to planned Cycle 1 Day 1)
* Parts C (Dose Escalation) and D (Dose Expansion): Combination Cohorts:
* Participants with active chronic inflammatory bowel disease (ulcerative colitis, Crohn disease) and participants with a history of bowel obstruction or gastrointestinal perforation within 6 months prior to planned Cycle 1 Day 1
* Participants who previously received topoisomerase 1 inhibitors or antibody-drug conjugates containing a topoisomerase 1 inhibitor
* Known severe intolerance or life-threatening hypersensitivity reactions to humanized monoclonal antibodies or intravenous (IV) immunoglobulin preparations; any history of anaphylaxis; history of human anti-human antibody response