• Patients must have pathologically or cytologically confirmed metastatic urothelial bladder carcinoma (Arm A) or other metastatic solid malignancy (Arm B) and MLL4-protein (KMT2D-gene) and UTX-protein (KDM6A-gene) or MTAP loss of function mutation including but not limited to single nucleotide variant (SNVs) that cause truncation, copy number variations (CNVs), and indels confirmed by next generation sequencing or immunohistochemistry techniques

• Patients must have at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1), measured preferably by computed tomography (CT) scan

• Patients who have received any prior neoadjuvant or systemic chemotherapy are eligible.

⁃ Notes:

∙ Patients must have progressive disease despite two prior lines of therapy in the metastatic setting unless the patient was not suitable for an approved second line regimen due to intolerance or another clinical factor;

‣ Treatment cannot have included prior pemetrexed. Any prior intravesical therapy, or immunotherapy is allowed. At least 4 weeks (28 days) wash-out period 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 0-2

• Absolute neutrophil count (ANC) ≥ 1,500/mcL (growth factor allowed and can be added at the discretion of the treating oncologist)

• 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 ≥ 45 mL/min/1.73 m\^2 using the standard Cockcroft and Gault formula

• Patients must have the ability to comply with the administration of supplemental therapies including folic acid, vitamin B12 and steroids as directed by study team and as per standard of care and institutional standards and practice for pemetrexed use

• Patients must be able swallow oral medication or not have problems/diseases that affect absorption or oral medication

• 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 was previously done 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 the lab has been completed previously as part of the patient's health care, then 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 was previously done as part of the patient's health care, it should be documented for eligibility

• 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. For this reason, patients of child-bearing potential (POCBP) and their partners with sperm-producing reproductive capacity must agree to use adequate contraception from time of informed consent, for the duration of study participation, and for 180 days following completion of pemetrexed therapy. Should a POCBP become pregnant or suspect they are pregnant while they or their partner are participating in this study, they should inform their treating physician immediately. Patients with sperm-producing reproductive capacity (PWSPRC) treated or enrolled on this protocol must also agree to use adequate contraception with partners of childbearing potential from time of informed consent, for the duration of study participation, and 180 days after completion of administration

⁃ Note: A POCBP is any patient (regardless of gender, sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) 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 must have a negative pregnancy test prior to registration on study

• The ability to interrupt nonsteroidal anti-inflammatory drugs (NSAIDS) or aspirin at higher dose (\> 1.3 g per day) 2 days before (5 days for long-acting NSAIDs), the day of, and 2 days following administration of pemetrexed

• Patients must be able to understand and voluntarily sign a written informed consent and willing and able to comply with the protocol requirements including scheduled visits, treatment plan, laboratory tests and other study procedures