Testing the Anti-cancer Drug, Rogaratinib (BAY 1163877), for Treatment of Advanced Sarcoma With Alteration in Fibroblast Growth Factor Receptor (FGFR 1-4), and in Patients With SDH-deficient Gastrointestinal Stromal Tumor (GIST)

Inclusion Criteria: * Participant must have histologically confirmed sarcoma with FGFR alteration identified by next-generation sequencing profiling with the exception of SDH-deficient GIST who can be enrolled regardless of FGFR status. Initial testing can be performed on archival tissue, if available. Patients must have locally advanced or metastatic disease that is not amenable to surgery * Presence of measurable disease: Patient must have measurable disease * Patients must have progressed following at least one standard prior chemotherapy regimen with the exception of SDH-deficient GIST for which there is no standard of care * Participant must be willing to undergo pre-treatment biopsy if disease site is amenable to biopsy and low risk for the biopsy procedure. If biopsy is not possible, eligibility may be approved after discussion with the Study Chair. Of note, a minimum of 15 participants in each arm open to stage 2 should have disease amenable to biopsy. For those arms open in stage 1, all patients should have biopsiable disease. * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of rogaratinib (BAY 1163877) in patients \<18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Hemoglobin \>= 8.0 g/dL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (…