Gemcitabine and Cisplatin With Ivosidenib or Pemigatinib for the Treatment of Unresectable or Metastatic Cholangiocarcinoma

Inclusion Criteria: * Histopathological diagnosis (fresh) or banked tumor biopsy sample collected within the last 3 years from the registration date consistent with nonresectable or metastatic cholangiocarcinoma and are not eligible for curative resection, transplantation, or ablative therapies * Documented disease without any evidence of progression following at least 3 cycles of standard-of-care chemotherapy including gemcitabine and cisplatin as part of first-line systemic therapy; NOTE: Only patients receiving standard-of-care chemotherapy including gemcitabine and cisplatin as first-line therapy for unresectable or metastatic cholangiocarcinoma will be permitted to enroll in this trial. Prior systemic adjuvant chemotherapy is allowed as long as there was no evidence of recurrence within 6 months of completing the adjuvant therapy * Molecular testing result from Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory (using fresh tumor biopsy or most recent banked tumor tissue available) confirming that the tumor tissue has at least one of the following: * IDH1 gene mutation (R132C/L/G/H/S mutation) * FGFR2 gene alteration * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 * Life expectancy \>= 3 months * At least one evaluable and measurable lesion by RECIST criteria prior to beginning chemotherapy with gemcitabine and cisplatin * NOTE: Subjects who have received prior local therapy (including but not limited to embolization, chemoembolization, radiofrequency ablation, hepatic arterial infusion, or radiation therapy) are eligible provided measurable disease falls outside of the treatment * Recovered from toxicities associated with prior anticancer therapy to baseline unless stabilized under medical management * Absolute neutrophil count \>= 1,500/mm\^3 (obtained =\< 21 days prior to registration) * Platelet count \>= 100,000/mm\^3 (obtained =\< 21 days prior to registration) * Hemoglobin \>= 8 g/dL (obtained =\< 21 days prior to registration) * Serum total bilirubin =\< 2.0 x upper limit of normal (ULN), unless considered due to Gilbert's disease. If Gilbert's disease or disease involving liver, serum total bilirubin =\< 2.5 x ULN (obtained =\< 21 days prior to registration) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN or =\< 5.0 x ULN in the presence of liver metastases (obtained =\< 21 days prior to registration) * Serum creatinine \< 1.5 x ULN OR creatinine clearance \>= 50 mL/min based on the Cockcroft-Gault glomerular filtration rate (GFR) estimation (obtained =\< 21 days prior to registration) * Serum phosphate =\< institutional ULN and potassium within institutional normal range for Arm B only (obtained =\< 21 days prior to registration) * NOTE: Supplemental potassium may be used to correct potassium prior to registration * Negative serum pregnancy test done =\< 7 days prior to registration for women of childbearing potential only * NOTE: Females of reproductive potential are defined as sexually mature women who have not undergone a hysterectomy, bilateral oophorectomy, or tubal occlusion or who have not been naturally postmenopausal (i.e., who have not menstruated) for \>= 24 consecutive months (i.e., have not had menses at any time in the preceding 24 consecutive months) * Women of reproductive potential and fertile men must agree to use 2 effective forms of contraception (including at least 1 barrier form) from the time of giving informed consent throughout the study and for 90 days (both females and males) following the last dose of study drug * NOTE: Effective forms of contraception are defined as hormonal oral contraceptives, injectables, patches, intrauterine devices, intrauterine hormone-releasing systems, bilateral tubal ligation, condoms with spermicide, or male partner sterilization * Able to understand and willing to sign the informed consent form * NOTE: A legally authorized representative may consent on behalf of a subject who is otherwise unable to provide informed consent if acceptable to and approved by the site's Institutional Review Board (IRB)/Independent Ethics Committee (IEC) * Able to comply with scheduled visits, treatment plans, procedures, and laboratory tests, including serial peripheral blood sampling during the study * Willing to provide blood samples for correlative research purposes Exclusion Criteria: * Prior therapy with either an IDH inhibitor or selective FGFR inhibitor * IDH inhibitors: ivosidenib, FT-2012, etc. * FGFR inhibitors: pemigatinib, BGJ-398, TAS-120, ARQ 087, or derazantinib, etc. * Progressive disease as best response on current standard-of-care chemotherapy including gemcitabine and cisplatin * Known toxicity to standard-of-care chemotherapy including gemcitabine and cisplatin requiring cessation of this therapy * Received radiotherapy to metastatic sites of disease =\< 2 weeks prior to registration * Underwent hepatic radiation, chemoembolization, or radiofrequency ablation =\< 4 weeks prior to registration * Known symptomatic brain metastases requiring steroids * NOTE: Subjects with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to study entry, have discontinued corticosteroid treatment for these metastases for at least 4 weeks and have radiographically stable disease for at least 3 months prior to registration * NOTE: Up to 10 mg per day of prednisone equivalent will be allowed * Other active malignancy =\< 5 years prior to registration. EXCEPTIONS: * Non- melanoma skin cancer unless stage 1a or carcinoma-in-situ of the cervix * Breast cancer with ongoing hormone therapy being administered as adjuvant therapy * NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment * Major surgery =\< 4 weeks prior to registration or have not recovered from post-surgery toxicities * Any of the following because this study involves investigational agents whose genotoxic, mutagenic, and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Arm A: Use of strong CYP3A4 inducers or strong or moderate CYP3A4 inhibitors. In addition, sensitive CYP3A4 substrate medications with a narrow therapeutic window, unless they can be transferred to other medications =\< 4 days or 5 half-lives (whichever is shorter) prior to registration * Arm B: Use of strong CYP3A4 inducers or inhibitors or moderate CYP3A4 inducers * NOTE: Study principal investigator (PI) approval is needed if continued use of CYP3A4 inducers or inhibitors. Approval can be obtained via email (documentation of approval/eligibility needed) * For Arm B only: Current evidence of clinically significant corneal (including but not limited to bullous/band keratopathy, corneal abrasion, inflammation/ulceration, and keratoconjunctivitis) or retinal disorder (including but not limited to central serous retinopathy, macular/retinal degeneration, diabetic retinopathy, retinal detachment) as confirmed by ophthalmologic examination * Known history and/or current evidence of ectopic mineralization/ calcification, including but not limited to soft tissue, kidneys, intestine, myocardia, or lung, excepting calcified lymph nodes and asymptomatic arterial or cartilage/tendon calcification for Arm B only * Known history of hypovitaminosis D requiring supraphysiologic doses to replenish the deficiency for Arm B only * NOTE: Subjects receiving vitamin D food supplements are allowed * Active infection requiring systemic anti-infective therapy or with an unexplained fever \> 38.5 degrees Celsius (C) =\< 7 days of registration * NOTE: At the discretion of the investigator, subjects with tumor fever may be enrolled * Any known hypersensitivity to any of the components of ivosidenib or pemigatinib * Significant, active cardiac disease =\< 6 months prior to registration, including * New York Heart Association (NYHA) class III or IV congestive heart failure * Myocardial infarction * Unstable angina * Stroke * Have a heart-rate corrected QT interval (using Fridericia's formula) (QTcF) \>= 450 msec or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) * Note: Bundle branch block and prolonged QTcF interval are permitted with approval of the medical monitor * Taking medications that are known to prolong the QT interval, unless they can be transferred to other medications \>= 5 half-lives prior to registration or unless the medications can be properly monitored during the study * Note: If equivalent medication is not available, QTcF should be closely monitored * Known active hepatitis B (hepatitis B virus \[HBV\]) or hepatitis C (hepatitis C virus \[HCV\]) infections, known positive human immunodeficiency virus (HIV) antibody results, or acquired immunodeficiency syndrome (AIDS) related illness * NOTE: Subjects with a sustained viral response to HCV or immunity to prior HBV infection will be permitted. Subjects with chronic HBV that is adequately suppressed per institutional practice will be permitted * NOTE: HBV, HCV, and/or HIV testing is not required prior to trial registration * Any other acute or chronic medical or psychiatric condition, including recent (=\< 12 months of registration) or active suicidal ideation or behavior, or a laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the subject inappropriate for entry into this study * Inability or unwillingness to swallow ivosidenib or pemigatinib or have significant gastrointestinal (GI) disorder(s) that could interfere with absorption, metabolism, or excretion * NOTE: Gastroesophageal reflux disease under medical treatment is allowed (assuming no drug interaction potential) * Have been committed to an institution by virtue of an order issued either by the judicial or administrative authorities * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm