A Precision Medicine Approach (SMMART-ACT) for the Treatment of Patients With Advanced Sarcoma, Prostate, Breast, Ovarian or Pancreatic Cancer

Inclusion Criteria: * PRE-SCREENING: Written informed consent prior to any Pre-Screening activities, study-specific procedures or interventions * PRE-SCREENING: At least 18 years of age at time of informed consent. Persons of all gender identities, biological sexes, races, and ethnicities will be included * PRE-SCREENING: A diagnosis of advanced sarcoma or advanced prostate, breast, ovarian, or pancreatic cancer. Change in an individual's cancer can be tracked objectively according to the Prostate Cancer Working Group 3 (PCWG3) criteria for prostate cancer, and Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 criteria for sarcomas and breast, ovarian, and pancreatic cancers * PRE-SCREENING: Biospecimen collection, as per institutional standards, must be consented to and collection must be feasible, with the following exceptions for tissue collections: * Individuals with a prior tumor tissue sample with successful SMMART-Clinical Analytics Platform (CAP) assays, collected within the last 90 days, may be eligible, so long as ≤ 1 treatment has been received within ≤ 90 days of that biopsy * PRE-SCREENING: Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 * PRE-SCREENING: Physician-assessed life expectancy of ≥ 6 months * PRE-SCREENING: Additional eligibility criteria specific to their disease must also be met * PRIMARY TREATMENT: Documented progression after at least 1 line of prior therapy for advanced disease. If recurrence occurred within 6 months of the last dose of an adjuvant/neoadjuvant therapy, that adjuvant/neoadjuvant therapy will count as 1 line of therapy * PRIMARY TREATMENT: SMMART-ACT tumor board recommendation of at least one SMMART-ACT therapy regimen defined within this protocol, based on the board's review of SMMART-CAP results on a pre-screening biopsy * PRIMARY TREATMENT: Absolute neutrophil count (ANC) ≥ 1,500/uL (1.5 K/cu mm) (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Platelets ≥ 100,000/uL (100 K/cu mm) (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Hemoglobin ≥ 9 g/dL (or ≥ 5.6 mmol/L) (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) ≤ 1.5 x institutional upper limit of normal (ULN) (institutional upper limit of normal \[IULN\]) OR ≥ 50 mL/min/1.73 m\^2 (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * Creatinine clearance should be calculated per institutional standard. For participants with a baseline calculated creatinine clearance below normal institutional laboratory values, a measured baseline creatinine clearance should be determined. Individuals with higher values felt to be consistent with inborn errors of metabolism will be considered on a case-by-case basis. * Creatinine clearance of \> 30 mL/min may be considered given that renal toxicity is not at increased risk and excretion is not major route of clearance for any chosen SMMART-ACT therapeutic * PRIMARY TREATMENT: Total bilirubin ≤ 1.5 x IULN OR direct bilirubin ≤ IULN for individuals with total bilirubin levels \> 1.5 x IULN (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/ Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x IULN (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: International normalized ratio (INR) or prothrombin time (PT) ≤ 1.5 x ULN, unless individual is receiving anticoagulant therapy, as long as PT or partial thromboplastin time (PTT) is within intended therapeutic range of intended anticoagulant therapy (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Activated partial thromboplastin time (aPTT) or PTT ≤ 1.5 x ULN, unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended anticoagulant therapy (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * PRIMARY TREATMENT: Body mass index (BMI) \> 16.0 and \< 35.0 kg/m\^2 (assessed at primary \[post pre-screening\] screening, or by the time that study intervention commences) * Participants with a BMI of ≥ 30.0 will use ideal body weight indices in calculating the delivery of agents that are dosed based upon body surface area (i.e., mg agent/meter squared) or weight (i.e., mg agent/kg body weight) * PRIMARY TREATMENT: Toxicities due to prior therapies should be resolved to baseline or grade 1 (per Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5.0) before administration of study intervention. The following exceptions are permitted: * Alopecia, fatigue, and lymphopenia due to prior therapies. * Toxicities attributed to prior anti-cancer therapy that are not expected to resolve and to result in long lasting sequelae (e.g., neuropathy after platinum-based therapy), may be permitted * PRIMARY TREATMENT: Palliative radiation therapy completed ≥ two weeks prior to start of SMMART-ACT treatment to a measurable disease lesion(s) * PRIMARY TREATMENT: Study intervention-specific eligibility criteria for the intended, recommended therapy must also be met * CANCER-SPECIFIC CRITERIA (BREAST CANCER): Lesion(s) remain measurable after systemic therapies, as follows: * At least one prior line of pharmacological therapy for hormone receptor (HR) positive, human epidermal growth factor receptor 2 (HER2)-negative disease. * At least one prior line of targeted therapy for HER2-positive disease * At least one prior line of combination therapy for triple negative disease lacking a BRCA1/2 mutation. * At least one prior line of therapy with a PARP inhibitor for triple negative disease with a BRCA1/2 mutation Exclusion Criteria: * PRE-SCREENING: Evidence of active malignancy of another cancer with a natural history or treatment history that may affect safety or efficacy assessments of this study or impose unacceptable risk to the participant. Guiding examples for those who can be enrolled include: individuals who have been disease free for ≥ two years; cancers with high cure rates (e.g., prior history of stage 1 rectal cancer and currently otherwise disease free); adequately treated, localized nonmelanomatous skin cancer * PRE-SCREENING: Absence of biopsiable lesion, AND unavailable/insufficient archival tissue * PRIMARY TREATMENT: Any brain/central nervous system (CNS) metastasis that progresses within ≤ four weeks of CNS directed treatment as ascertained by clinical examination(s) and MRI or CT during the main eligibility screening period * PRIMARY TREATMENT: One or more new, active brain/CNS metastasis or the presence of known leptomeningeal disease (LMD) that requires immediate treatment. If treatment within the first cycle of therapy is unlikely to be required, enrollment may be considered, as per the investigator * PRIMARY TREATMENT: Concurrent forms of anti-cancer therapy that have the potential to interfere with efficacy and safety assessments or that may pose increased risk to the participant while on a SMMART-ACT treatment, and as per the investigator (Select hormone therapies are allowed) * PRIMARY TREATMENT: More than one intervening line of therapy for treatment of their cancer since the time of the pre-screening biopsy, exclusive of most maintenance hormone therapies * Note: Participants who have a pre-screening biopsy while receiving a standard of care (SOC) treatment will not be eligible if they receive any additional lines of treatment prior to the start of SMMART-ACT treatment. This treatment will count as one line of intervening therapy * PRIMARY TREATMENT: Untreated and/or uncured hepatitis C virus (HCV) infection, as evidenced by detectable hepatitis B core (HBC) ribonucleic acid (RNA) by polymerase chain reaction (PCR). Prior treatment, concurrent treatment, and natural resolution of HCV infection are not exclusionary given (1) no risk for hepatic decompensation and (2) the intended SMMART-ACT treatment is not expected to exacerbate HCV infection * PRIMARY TREATMENT: Uncontrolled intercurrent illness and infection that may interfere with planned treatment, including, but not limited to, the following: * Symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III or IV), * Unstable angina pectoris or coronary angioplasty, or stenting within \< six months prior to enrollment, * Cardiac arrhythmia (ongoing cardiac dysrhythmias of grade ≥ 2 \[National Cancer Institute (NCI) CTCAE v 5.0\]), * Conditions that require intra-cardiac defibrillators, * Known cardiac metastases, * History of abnormal cardiac valve morphology (≥ grade 2), * Chronic graft versus host disease (GVHD) or immunosuppressive therapy for the control of GVHD * PRIMARY TREATMENT: Severe infection within \< four weeks prior to initiation of study therapy, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * PRIMARY TREATMENT: Inability or unwillingness to take oral medication (only for assigned oral study interventions) * PRIMARY TREATMENT: History of allergy to an assigned study agent or its excipients * PRIMARY TREATMENT: Current pregnancy, current breastfeeding, or unwillingness to not breastfeed while receiving study drug(s) or for the minimum required time after the last dose of study drug(s) as specified by the SMMART-ACT drug agents * PRIMARY TREATMENT: Any condition that, in the opinion of the investigator, could jeopardize the participant's safety or adherence to the study protocol * CANCER-SPECIFIC CRITERIA (PROSTATE CANCER): If the screening bone scan shows a "superscan" participants will be excluded from participation. This is defined as an intense symmetric activity in the bones and diminished renal parenchymal activity, such that the presence of additional metastases in the future could not be evaluated