Testing JNJ-42756493 (Erdafitinib) as Potentially Targeting Treatment in Cancers With FGFR Mutations or Fusions (MATCH - Subprotocol K2)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol * Patients must fulfill all eligibility criteria outlined in the MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7) * Patients must have FGFR mutation or fusion as determined via the MATCH Master Protocol * Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block) * Patients must not have known hypersensitivity to JNJ-42756493 (erdafitinib) or compounds of similar chemical or biologic composition. * Patients with current evidence of corneal or retinal disorder/keratopathy are excluded * Patients must not be currently using medications that can elevate serum phosphorous and/or calcium levels * Medications that increase serum calcium should be avoided. Over the counter calcium supplements, antacids that contain calcium (Tums) and Vitamin D supplements (cholecalciferol and ergocalciferol) should be avoided. Prescription medications including lithium, hydrochlorothiazide and chlorthalidone must be used with caution * Medications that increase serum phosphate should be avoided. Over the counter laxatives that contain phosphate such as Fleets Oral or Fleets enema and Miralax should be avoided * Patients with a history of hyperphosphatemia will be excluded * Patients may not have received strong inhibitors or potent inducers of CYP3A within 2 weeks before the first dose of study treatment. Patients with inability to discontinue treatment with a strong CYP3A4 and/or CYP2C9 inhibitor or inducer prior to start of treatment are excluded * Patients who have previously received treatment with a FGFR targeted inhibitor are excluded. Such inhibitors include AZD4547, BGJ398, BAY1163877 and LY2874455). Prior non-selective FGFR inhibitor treatment (e.g. Pazopanib, dovitinib, ponatinib, brivanib, lucitanib, lenvatinib) are allowed * Patients must not have any history of or current evidence of renal or endocrine alterations of calcium/phosphate homeostasis, or history of or current evidence of extensive tissue calcification (by evaluation of the clinician), including but not limited to, the soft tissue, kidneys, intestine, myocardium and lung with the exception of calcified lymph nodes and asymptomatic vascular calcification per investigators' judgment * Patients with transitional cell carcinoma of the bladder and /or urothelial tract are not eligible. These patients are encouraged to enroll in the ongoing disease-specific studies * Patients with impaired renal function (glomerular filtration rate \[GFR\] \< 60 mL/min) are excluded. GFR should be assessed by direct measurement (i.e., creatinine clearance or ethyldediaminetetraacetate) or, if not available, by calculation from serum/plasma creatinine (Cockcroft-Gault formula) * Patients with persistent phosphate level \> ULN during screening (within 14 days of treatment and prior to Cycle 1 Day 1) and despite medical management are excluded * Patients with a history of or current uncontrolled cardiovascular disease as stated below are excluded: * Unstable angina, myocardial infarction, or known congestive heart failure Class II-IV within the preceding 12 months; cerebrovascular accident or transient ischemic attack within the preceding 3 months, pulmonary embolism within the preceding 2 months • Any of the following: sustained ventricular tachycardia, ventricular fibrillation, Torsades de Pointes, cardiac arrest, Mobitz II second degree heart block or third degree heart block; known presence of dilated, hypertrophic, or restrictive cardiomyopathy * Patients with impaired wound healing capacity defined as skin/decubitus ulcers, chronic leg ulcers, known gastric ulcers, or unhealed incisions are excluded * Female subjects (of child-bearing potential and sexually active) must use medically acceptable methods of birth control (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of the study, and for 4 months after the last intake of study drug. Male subjects (with a partner of child-bearing potential) must use a condom with spermicide when sexually active and must not donate sperm from the first dose of study drug until 5 months after the last dose of study drug