Pemetrexed and Avelumab in Treating Patients With MTAP-Deficient Metastatic Urothelial Cancer

Inclusion Criteria: * Patients must have histologic confirmation of MTAP-deficient metastatic urothelial carcinoma. MTAP-deficiency must be verified by institutional Clinical Laboratory Improvement Act (CLIA)-certified immunohistochemistry (IHC). Histological variants such as glandular, squamous, sarcomatoid, micropapillary, plasmacytoid, and small cell changes will be allowed for this trial if these tumors are MTAP-deficient. * Patients can be considered for second line of therapy (after chemotherapy or immune checkpoint inhibitor with PD-\[L\]1 agent) or for third line of therapy (can have previously received chemotherapy and immune checkpoint inhibitor with PD-\[L\]1 blockade). Any prior intravesical therapy is allowed and does not count as a prior line of therapy. * Patients who received methotrexate-containing chemotherapy (e.g. methotrexate/vinblastine/adriamycin/cisplatin \[MVAC\]) as neoadjuvant therapy or first-line systemic therapy at least 12 months prior will be allowed for this trial. * All patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 and tumors of sufficient sizes for biopsy. In general, liver and lung lesions should be at least 1.0 cm, and patients with lymph node-only disease should have lesions of \>= 1.5 cm in shortest dimension. Patients with disease confined to bone may be eligible if a measurable lytic defect is present. The study principal investigator (PI) is the final arbiter in question…