BMS-986504 in Combination With Pemetrexed for the Treatment of Metastatic Solid Tumors With MTAP Deletion

Inclusion Criteria: * COHORT A (INCLUDING SAFETY RUN IN, STAGE I AND STAGE II) AND COHORT B: * Patients must have pathologically or cytologically confirmed metastatic solid tumor of gastrointestinal origin with MTAP deletion including pancreatic cancer, biliary cancer, esophageal cancer and colon cancer (Cohort A) or other metastatic solid malignancy with MTAP deletion (Cohort B) confirmed by validated next generation sequencing tissue techniques only * NOTE: Both internal and external validated next generation sequencing (NGS) panels are acceptable * Progressive disease (PD) after one previous standard of care line of treatment * NOTE: symptoms from clinical evaluation for PD will be sufficient * Patients must have at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1, measured preferably by computed tomography (CT) scan * Note: Tumor lesions in a previously irradiated area are not considered measurable unless they show unequivocal progression * NOTE: There is no limit on previous treatment lines * Patients who have received any neoadjuvant or systemic chemotherapy are eligible * Note: treatment cannot have included prior pemetrexed unless in the case of non-small cell lung cancer (NSCLC) cancer type. Any prior intravesical therapy, or immunotherapy is allowed. At least 3 weeks (21 days) wash-out period from treatment since prior chemotherapy or radiation therapy or targeted agent is required * Patients must be aged ≥ 18 years * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Absolute neutrophil count (ANC) ≥ 1,500/mcL (growth factor allowed and can be added at the discretion of the treating oncologist * Growth factors are excluded from being used during the DLT observation period (cycle 1) unless they are being used to treat a grade 4 adverse event which will be counted as a DLT. If growth factors are being used for grade ≤ 3 toxicity, then patients will not be evaluable for DLT assessment * Hemoglobin (Hgb) ≥ 8.5 g/dL (without the need for transfusion within the previous one week) * Platelets (PLT) ≥ 100,000/mL (without the need for platelet transfusion within the previous one week) * Total bilirubin ≤ 1.5 x Institutional upper limit of normal (ULN), except subjects with Gilbert's syndrome or liver metastases, who must have a baseline total bilirubin ≤ 3.0 mg/dL * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 3 x institutional ULN or ≤ 5 x ULN if documented liver metastases are present * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN or ≤ 5 x ULN if documented liver metastases are present * Creatinine clearance ≥ 60 mL/min/1.73 m\^2 using the standard Cockcroft and Gault formula * Patients must have the ability to comply with folic acid, vitamin B12 and steroids as directed by study team and as per standard of care for pemetrexed use * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Pemetrexed is known to be teratogenic. Reproductive toxicology studies with MRTX1719 have not been performed. The investigator or designee shall counsel patients of childbearing potential (POCBP) participants and male (as assigned at birth) participants who are sexually active with POCBP on the importance of pregnancy prevention, the implications of an unexpected pregnancy, and the potential of fetal toxicity occurring due to transmission of study intervention present in seminal fluid to a developing fetus, even if the participant has undergone a successful vasectomy or if the partner is pregnant. If needed, participants should be advised to seek advice about egg or sperm donation and cryopreservation of germ cells before treatment * Patients of childbearing potential POCBP * A POCBP is any patient with an egg-producing reproductive tract who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * POCBP are not permitted to use hormonal contraceptive methods alone as a highly effective method of contraception and must use an additional non-hormonal highly effective method of contraception. POCBP 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 at least 6 months after the last dose of study intervention, or according to approved local product label requirements for pemetrexed, whichever is longer * POCBP participants must also agree not to donate eggs (ova, oocytes) for the purpose of reproduction for the same period * Male (as assigned at birth) participants will be required to always use a latex or other synthetic condom during any sexual activity (eg, vaginal, anal, oral) with POCBP, even if the participant has undergone a successful vasectomy or if the partner is pregnant or breastfeeding. Male (as assigned at birth) participants should continue to use a condom during the intervention period and for at least 6 months after the last dose of study intervention, or according to approved local product label requirements for pemetrexed, whichever is longer * POCBP partners of male (as assigned at birth) participants should be advised to use a highly effective method of contraception during the intervention period and for at least 6 months after the last dose of study intervention for the male participant, or according to approved local product label requirements for pemetrexed, whichever is longer * Male (as assigned at birth) participants 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 6 months after the last dose of study intervention, or according to approved local product label requirements for pemetrexed, whichever is longer * Male (as assigned at birth) participants must refrain from donating sperm during the intervention period and for at least 6 months after the last dose of study intervention, or according to approved local product label requirements for pemetrexed, whichever is longer * Breastfeeding partners of male (as assigned at birth) participants 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 * POCBP must have a negative pregnancy test prior to registration on study * The ability to interrupt nonsteroidal antiinflammatory drugs (NSAIDS) or aspirin at higher dose (\> 1.3 g daily) 2 days before (5 days for long-acting NSAIDs), the day of, and 2 days following administration of pemetrexed Exclusion Criteria: * STAGE I AND II, COHORT A (INCLUDING SAFETY RUN IN) AND B: * Patients who received prior pemetrexed containing chemotherapy (apart from NSCLC) * Patients with prior treatment with a PRMT5 or MAT2A inhibitor therapy * Patients with pre-existing clinically significant interstitial lung disease (ILD) * Patients who have had chemotherapy or radiotherapy ≤ 21 days prior to planned treatment start date. * Note: seven days or fewer of palliative radiotherapy for non-CNS disease, is permitted. No wash-out is required * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia and neuropathy per National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) v 5.0 * Patients who are receiving any other investigational agents or devices. Patients start of study treatment will be based on their discontinuation and recovery from clinically significant adverse events from their most recent therapy or intervention prior to study enrollment * Patients who have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to pemetrexed * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following: * Ongoing or active infection requiring systemic treatment * Symptomatic congestive heart failure * Unstable angina pectoris * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Patients with a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification * Note: To be eligible for this trial, patients should be class 2B or better * Patients with presence of third space fluid which cannot be controlled by drainage * Note: For patients who develop or have baseline clinically significant pleural or peritoneal effusions (on the basis of symptoms or clinical examination) before or during initiation of pemetrexed therapy, consideration should be given to draining the effusion prior to dosing. However, if, in the investigator's opinion, the effusion represents progression of disease, the patient should be discontinued from study therapy * Patients who are not able to understand and voluntarily sign a written informed consent and is not willing and able to comply with the protocol requirements including scheduled visits, treatment plan, laboratory tests and other study procedures * Patients who are pregnant or nursing * Patients with history of intestinal disease, inflammatory bowel disease, major gastric surgery, or other gastrointestinal conditions (eg, uncontrolled nausea, vomiting, malabsorption syndrome) likely to alter absorption of study treatment or result in inability to swallow oral medications * Patients with Fridericia's formula-corrected QT interval (QTcF) prolongation \> 480 msec, except for right bundle branch block, per the investigator's assessment * Patients with ongoing need for a medication with a known risk of Torsade's de Pointes that cannot be switched to an alternative treatment prior to study entry * Patients with ongoing need for a medication known as a strong inhibitor or strong inducer of cytochrome P450 3A4 (CYP3A4) and/or P-glycoprotein (P-gp) or a proton-pump inhibitor and potassium-competitive acid blockers that cannot be switched to an alternative treatment prior to study entry * NOTE: The following drug interaction databases and other literature can be utilized to determine the CYP3A4/P-gp inhibitors and inducers * Note: Please consult with the manufacturer for any uncertainties regarding potential CYP3A4 and P-gp modulators * Patients with inability to comply with restrictions and prohibited treatments * Patients taking any botanical preparation (e.g., herbal supplements or traditional Chinese medicines) intended to treat the disease under study within 4 weeks prior to treatment. The concurrent use of any botanical preparation is not permitted while on study * Patients with a known history of human immunodeficiency virus (HIV), infected patients on effective anti-retroviral therapy must have a viral load undetectable for 6 months prior to registration. Please note this lab is not a requirement for eligibility, however, if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients with a known history of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Please note this lab is not a requirement for eligibility; however if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients with a known history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with a known HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. Please note this lab is not a requirement for eligibility; however if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients who take live/attenuated vaccine received within 30 days of first treatment. The use of inactivated seasonal influenza vaccines (e.g., Fluzone®) will be permitted on study without restriction * Patient has not received the final dose of any of the following treatments/ procedures with the specified minimum intervals before first dose of study drug: * Surgery with general anesthesia - within 7 days of first dose of study drug * Surgery with local anesthesia - with 3 days of first dose of study drug