Pemigatinib + Afatinib in Advanced Refractory Solid Tumors

Inclusion Criteria: All Patients * Unresectable or metastatic, histologically confirmed advanced solid tumor, where standard curative or palliative measures are no longer effective or are not considered appropriate or safe in the opinion of the investigator. * FGFR1-3 fusion, rearrangement, activating mutation, or FGFR2 extracellular domain in-frame deletions on tumor profiling in tumor tissue as determined by testing routinely performed at a Clinical Laboratory Improvement Amendments (CLIA) or other similarly certified laboratory. If the FGFR alteration is present on circulating tumor DNA (ctDNA) analysis alone, the patient may be eligible with principal investigator approval. Additional mutations may be considered with principal investigator approval. * Eastern Cooperative Oncology Group (ECOG) 0-1. * At least 18 years of age. * Ability to swallow tablets. * Life expectancy \>/=3 months * Ability to comply with outpatient treatment, laboratory monitoring, and required clinic visits for the duration of study participation. * Patients with cholangiocarcinoma must have adequate biliary drainage (per investigator's discretion), with no evidence of ongoing infection. * Willingness of men and women of reproductive potential to observe conventional and effective birth control for the duration of treatment and for 3 months following the last dose of study treatment. * Measurable or non-measurable disease as determined by RECIST 1.1. * Adequate organ function defined as: * ALT or AST ≤ 3 × the ULN in the absence of liver metastases, OR ≤ 5 × ULN with documented liver metastases * Total bilirubin ≤ 2.0 × ULN in the absence of Gilbert's Disease, OR ≤ 3 × ULN with Gilbert's Disease provided direct bilirubin is ≤ ULN * Serum Creatinine ≤ 1.5 × ULN OR calculated creatinine clearance ≥ 60ml/min * Hemoglobin ≥ 9 g/dL (≥ 90 g/L) * Absolute Neutrophil Count ≥ 1.5 x 109/L * Platelets ≥ 75 x 109/L * INR or PT, aPTT or PTT ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy * NOTE: Transfusions to increase a patient's hemoglobin level or initiation of erythropoietin or G-CSF therapy to meet enrollment criteria are not allowed in the 14 days preceding the first dose of study drug. If a patient receives transfusions, erythropoietin, or G-CSF therapy ≥ 14 days prior to the first dose, the hematologic criteria listed above must be met following the 14-day window and prior to the first dose of study therapy Dose expansion cohort 1: Patients should fulfill the eligibility criteria above for all patients in addition to the following: * Histologically or cytologically confirmed diagnosis of advanced or metastatic cholangiocarcinoma * No prior treatment with a selective FGFR inhibitor treatment * FGFR2 fusion, in-frame rearrangement, or extracellular domain in-frame deletion on tumor profiling in tumor tissue as determined by testing routinely performed on tumor biopsy at a CLIA or other similarly certified laboratory. If the FGFR alteration is present on ctDNA analysis alone, the patient may be eligible with principal investigator approval. * An archived tumor tissue sample is available in patients not undergoing fresh tumor biopsy. Patients who do not have adequate archival tumor tissue available are required to undergo a fresh tumor biopsy. If a fresh biopsy cannot be safely performed, the patient may be eligible with principal investigator approval. Dose expansion cohort 2: Patients should fulfill the eligibility criteria above for all patients in addition to the following: * Histologically or cytologically confirmed diagnosis of advanced or metastatic cholangiocarcinoma * Prior FGFR inhibitor treatment at any time prior to treatment start is required * FGFR2 fusion, in-frame rearrangement, or extracellular domain in-frame deletion for which they derived clinical benefit (objective response of any duration or stable disease for at least 6 months) from prior FGFR inhibitor therapy, as determined by testing routinely performed on tumor biopsy at a CLIA or other similarly certified laboratory. If the FGFR alteration is present on ctDNA analysis alone, the patient may be eligible with principal investigator approval * An archived tumor tissue sample after progression on or intolerance of prior FGFR inhibitor available in patients not undergoing fresh tumor biopsy. Patients who do not have adequate archival tumor tissue available are required to undergo a fresh tumor biopsy. If a fresh biopsy cannot be safely performed, the patient may be eligible with principal investigator approval. Exclusion Criteria: * Known hypersensitivity to afatinib or pemigatinib or excipients of pemigatinib * For patients treated with a prior FGFR inhibitor, those with known activating mutation(s) in the FGFR2 kinase domain on ctDNA or biopsy analysis within 8 weeks of start of study drugs; activating mutations in the FGFR2 kinase domain seen on ctDNA or biopsy analysis prior to the 8-week timepoint may be allowed after discussion with the study PI. * Systemic or liver-directed anticancer therapy within 2 weeks; or anticancer monoclonal antibody within 4 weeks prior to planned start of pemigatinib and afatinib. * Patient has adverse events from prior therapy that have not resolved to ≤ grade 1; exceptions for non-clinically meaningful adverse events (AEs) can be made with input from the principal investigator. * Major surgery within 4 weeks prior to planned start of pemigatinib and afatinib (tumor biopsy, biliary stent or catheter placement, and feeding tube placement are not considered major surgical procedures). * Received prior palliative non-CNS radiation within 2 weeks or extended-field radiation administered within 4 weeks of first dose of study drug. Subjects must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. Fibrotic pulmonary disease from prior radiotherapy is permissible with approval of the study PI. * Known pre-ex