A Study of BMS-986504 With Standard-of-Care Therapy for People With Solid Tumor Cancer

Inclusion Criteria: * Documentation of Disease: * Patients must have pathologic confirmation of one of three diseases: * Diffuse pleural mesothelioma (DPM) * Gastroesophageal carcinoma (GEC) including adenocarcinoma or squamous cell carcinoma of the esophagus, gastroesophageal junction, or stomach. * PD-L1 CPS ≥1 (using clone 73-10, DAKO) * HER2 overexpression negative (using clone 4B5, Ventana): HER2 IHC 0-1+, or HER2 2+ with ISH showing HER2:CEP17 ratio \<2 and average HER2 copy number \<6.0 signals/cell * Urothelial carcinoma (UC) * Archival tissue is acceptable * Metastatic or advanced/unresectable disease: * For Diffuse Pleural Mesothelioma (DPM) and Gastroesophageal Carcinoma (GEC )cohorts: no prior systemic treatment for metastatic disease * Patients with metastatic disease after treatment for localized GEC may have received prior systemic therapy (chemotherapy and/or chemoradiation) if \>6 months have elapsed between the end of therapy and registration. * One prior cycle of standard-of-care therapy alone without BMS-986504 or other MTAP inhibitors (ipi/nivo for DPM, FOLFOX + nivo for GEC) is acceptable with PI approval. * For UC cohort: must have received at least 1 prior line of treatment without prior gemcitabine (prior tx with Gem+Platinum in the perioperative setting is permitted if at least 12 months have elapsed from trial enrollment) * Patients with recurrent disease within 1 year of completion of prior perioperative systemic therapy are eligible with PI approval. * One prior cycle of standard-of-care therapy alone with gemcitabine + platinum, without BMS-986504 or other MTAP inhibitors, is acceptable with PI approval. * Confirmation of MTAP deletion by either IHC or NGS: * MTAP deletion must be detected by either IHC and/or NGS (including FACETS), done on tumor tissue (not blood): * IHC (using antibody 1813, NBP2-75730, Novus Biologicals)30 * IHC staining showing loss of MTAP expression * Tissue-based NGS options * MSK-IMPACT version 7 or beyond showing homozygous MTAP copy number loss * FACETS showing homozygous deletion * Other CLIA-approved commercial Template Version: 1-21-25 * Full report must be available for review and confirmation * Cases with discordant results between NGS and IHC, in which one test shows MTAP loss/MTAP del and the other shows MTAP intact, are acceptable with PI approval * Measurable disease per RECIST v 1.1 (or, for DPM cohort, by either RECIST v 1.1 or modified RECIST \[mRECIST\] for mesothelioma31) * No contraindications to receiving other standard-of-care agents per package inserts (and see Appendix IV), and per the discretion of the PI: * DPM: Ipilimumab + nivolumab * GEC: FOLFOX (5-FU, leucovorin, and oxaliplatin) + nivolumab * UC: Gemcitabine + platinum (carboplatin or cisplatin) * Age ≥ 18 * KPS ≥ 70/ECOG \<1 * Reproductive Status: * Female participants of child-bearing potential (as assigned at birth) must have a negative highly sensitive urine or serum (as required by local regulations) pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin) within 24 hours prior to the start of study intervention. * If a urine test cannot be confirmed as negative (eg, an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. * Female participants of child-bearing potential (as assigned at birth) must agree to use a combination of a hormonal and a non-hormonal contraceptive method or a non-hormonal method alone that is highly effective (with a failure rate of \< 1% per year)during the intervention period and for 14 months (for females) after the last dose of study intervention (or longer if required by institutional guidelines) * Female participants of child-bearing potential (as assigned at birth) must also agree not to donate eggs (ova, oocytes) for the purpose of reproduction for the same period. * If needed, these participants should be advised to seek advice about egg donation and cryopreservation of germ cells before treatment. * Female participants (as assigned at birth) are deemed to be without child-bearing potential if they meet one of the following criteria: * Postmenopausal for at least 1 year before the screening visit * Permanently sterile (undergone a hysterectomy, bilateral salpingectomy or bilateral oophorectomy) with surgery at least 1 month before the first dose of study drug or confirmed by follicle stimulating hormone (FSH) test \> 40 mIU/mL and estradiol \< 40 pg/mL (\<140 pmol/L) * Male participants (as assigned at birth) will be required to always use a latex or other synthetic condom during any sexual activity (eg, vaginal, anal, oral) with a female of childbearing potential, even if the participant has undergone a successful vasectomy or if the partner is pregnant or breastfeeding. Male participants (as assigned at birth) should continue to use a condom during the intervention period and for at least 11 months after the last dose of study intervention (or longer if required by institutional guidelines). * Male participants must refrain from donating sperm during the intervention period and for at least 11 months after the last dose of study intervention (or longer if required by institutional guidelines). * If needed, male participants should be advised to seek advice about sperm donation and cryopreservation of germ cells before treatment. * Individuals of child-bearing potential who are partners of male participants should be advised to use a highly effective method of contraception during the intervention period and for at least 11 months after the last dose of study intervention for the male participant * Male participants (as assigned at birth) with a pregnant or breastfeeding partner must agree to remain abstinent from sexual activity or use a male condom during any sexual activity (eg, vaginal, anal, oral), even if the participant has undergone a successful vasectomy, during the intervention period and for at least 11 months after the last dose of study intervention * Breastfeeding partners of male participants (as assigned at birth) should be advised to consult their health care provider about using appropriate highly effective contraception during the time the male participant is required to use condoms * Recovery from the adverse effects of prior therapy at the time of enrollment to baseline or ≤ Grade 1 (excluding alopecia, peripheral neuropathy, and parameters superseded by other eligibility criteria \[eg, hematology parameters\]). Note: Participants with prior endocrine adverse effects are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic. * Required organ function * Adequate hematologic function defined as follows: * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm\^3 * Platelets ≥ 100,000 cells/mm3 * Hemoglobin ≥ 8 g/dl * Adequate renal function defined as follows: * Creatinine clearance (CrCL) of ≥50 mL/min by the CKD-Epi creatinine equation * Adequate hepatic function defined as follows: * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (patients with known Gilbert's disease who have bilirubin level ≤ 3 x ULN may be enrolled) * AST and ALT ≤5 x ULN * Signed informed consent form (ICF) Exclusion Criteria: * Prior treatment with PRMT5i or MAT2Ai * Symptomatic CNS metastases * Patients with treated brain metastases are eligible if follow up brain imaging after CNS directed therapy shows no evidence of progression and the patient is on a stable dose of corticosteroids * Received palliative radiation therapy within 3 days prior to initiation of study treatment or definitive SRS including CNS SRS within 14 days prior to initiation of study treatment * Patients who have had major surgery within 3 weeks of start of study drug o Note: procedures such as biopsy, pleural catheter insertion, central venous catheter or other minor procedures are permitted * Any of the following cardiac abnormalities: * Unstable angina pectoris or myocardial infarction within 6 months prior to enrollment * Congestive heart failure ≥ NYHA Class 3 within 6 months prior to enrollment * Prolonged QTc \> 500 milliseconds or history of Long QT Syndrome * Child-Pugh class C liver cirrhosis * Ongoing medical illness not otherwise listed which would preclude study at the discretion of the PI * Inability to take medications PO (BMS-986504 cannot be taken via gastrostomy tube), refractory nausea and vomiting, malabsorption, biliary shunt, significant bowel resection, or any other condition that significantly affects gut motility or absorption and would preclude adequate absorption of BMS-986504 in the opinion of the treating physician and/or PI * Ongoing need for a medication that is a strong inhibitor or strong inducer of cytochrome P450 (CYP) 3A4 and/or P-glycoprotein (P-gp) or proton-pump inhibitor that cannot be switched to alternative treatment prior to study entry * HIV, HBV, or HCV with detectable viral load * For patients with known HIV, HBV, and/or HCV infection: * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable with or without suppressive therapy * Patients with a history of HCV infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Active infection requiring parenteral antibiotic(s) * Pregnant or breastfeeding * Presence of another malignancy that could be mistaken for the malignancy under study during disease assessments. * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.