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-existing interstitial lung disease * Current hypovitaminosis D requiring supraphysiologic (eg 50,000 IU/weekly) to replenish the deficiency. Vitamin D supplements are allowed. * History and/or current evidence of clinically significant ectopic mineralization/calcification or non-tumor related alteration of calcium-phosphorus homeostasis. * History and/or current evidence of clinically significant corneal or retinal disorder confirmed by ophthalmological examination * Child-Pugh B and C cirrhosis * Chronic nausea, vomiting, or diarrhea considered to be clinically significant in the opinion of the investigator. This includes significant or recent gastrointestinal disorders with diarrhea as a major symptom * Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal absorption of the study drug. * Patients with a history of another primary malignancy that is currently clinically significant, and has potential for metastases or currently requires active intervention (except for gonadotropin-releasing hormone (GnRH) or luteinizing hormone-releasing hormone (LH-RH) agonists in prostate cancer or hormonal therapy in breast cancer * Have history of hepatic encephalopathy of any grade * Patients with ascites requiring serial paracenteses * Active central nervous system (CNS) metastases are not eligible. Patients with asymptomatic and treated brain metastases may participate provided that they are stable for ≥ 2 months. Patients with suspected or confirmed leptomeningeal disease are not eligible even if treated. Patients with glioblastoma multiforme (GBM) are not eligible. * Clinically significant, active cardiovascular disease such as uncontrolled hypertension, congestive heart failure New York Heart Association (NYHA) classification of 3, unstable angina or poorly controlled arrhythmia, or history of myocardial infarction within 6 months prior to planned start of pemigatinib and afatinib * Fridericia's corrected QT interval (QTcF) \> 480 ms on ECG conducted during Screening, or history of torsades de pointes or personal or family history of prolonged QT syndrome.Correction of suspected drug-induced QTcF prolongation can be attempted at the investigator's discretion and only if clinically safe to do so with either discontinuation of the offending drug or switch to another drug not known to be associated with QTcF prolongation. * Active uncontrolled systemic bacterial, viral, fungal or parasitic infection (except for fungal nail infection), or other clinically significant active disease process which in the opinion of the investigator and the sponsor-investigator makes it undesirable for the patient to participate in the trial. Screening for chronic conditions is not required. * Active hepatitis B virus (HBV) \-- Note: Controlled (treated) hepatitis will be allowed if they meet the following criteria: antiviral therapy for HBV must be given for at least 1 month prior to first dose of study drug, and HBV viral load must be less than 2000 IU/ml (104 copies/ml) prior to the first dose of study drug. Those on active HBV therapy with viral loads under 2000 IU/ml (104 copies/ml) should stay on antiviral therapy throughout the study treatment. * Known human immunodeficiency virus (HIV) and on anti-retroviral therapy for HIV(excluded due to potential drug-drug interactions between anti-retroviral medications and study treatment but HIV itself is not an exclusion). * Known or suspected active drug or alcohol use * Concomitant treatment with known strong p-gp inhibitor. * Use of any potent CYP3A4 inhibitors or inducers or moderate CYP3A4 inducers within 14 days or 5 half-lives (whichever is longer) before the first dose of study treatment. \-- Note: Moderate CYP3A4 inhibitors are not prohibited * Pregnancy during the study or within 30 days of the last dose of study intervention. Also excluded are any persons of childbearing potential, including men who are able to father a child, who are unwilling to use a medically acceptable method of contraception during the trial (see below section 3.3). Lactation and breastfeeding during the study or within 30 days of the last dose of study intervention is also not allowed. Female patients must have a negative pregnancy test (B-HCG test in urine or serum) prior to commencing study treatment. * Unable to swallow pills * Any other concomitant serious illness or organ system dysfunction which in the opinion of the investigator would either compromise patient safety or interfere with the evaluation of the safety of the study drug. Patients unable or deemed by the investigator as unlikely to comply with the protocol are also excluded.