mFOLFIRINOX Followed by Hepatic Arterial Infusion of Floxuridine and Dexamethasone With Systemic mFOLFIRI for Unresectable Liver-dominant Intrahepatic Cholangiocarcinoma

Inclusion Criteria: * Histologically confirmed intrahepatic cholangiocarcinoma (ICC; also variously reported as peripheral cholangiocarcinoma, cholangiolar carcinoma or cholangiocellular carcinoma) with confirmation of the pathologic diagnosis at Oregon Health \& Science University (OHSU) * Surgically unresectable liver-dominant ICC, or multifocal ICC considered surgically unresectable or resection is contraindicated * For liver-dominant ICC, disease must comprise \< 70% of the liver parenchyma, as defined by computed tomography (CT) liver segmental volumetrics * Limited extrahepatic disease * Clinical or radiographic evidence of metastatic disease to regional lymph nodes and limited extrahepatic disease to the lungs is permitted at the discretion of the principal investigator (PI) * Radiographically measurable hepatic disease per Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 criteria * Disease must be considered technically unresectable at the time of preoperative evaluation or radiographically multifocal as determined by hepatobiliary surgical oncologists * Participants should be treatment naive. Those previously treated with systemic chemotherapy (e.g., gemcitabine, cisplatin, or other investigational agents) may be eligible at the discretion of the PI * Participants with an Eastern Cooperative Oncology Group (ECOG) 0 or 1 status (Karnofsky \>= 60), and can be considered candidates for general anesthesia, abdominal exploration and hepatic artery pump placement * Participants with treated chronic hepatitis (e.g., treated hepatitis B virus \[HBV\], treated hepatitis C virus \[HCV\]) are eligible, but must be Child-Pugh class A * White blood cell (WBC) \>= 3000 cells/mm\^3 * Absolute neutrophil count (ANC) \>= 1500 cells/mm\^3 * Platelet count \>= 100,000/mm\^3 * International normalized ratio (INR) =\< 1.5 * Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR creatinine clearance \>= 40 ml/min (\> 0.675 ml/sec) using Cockcroft-Gault equation * Total bilirubin \< 1.5 mg/dL * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * Participants must be able to read, understand, and sign informed consent * Participants must be willing and able to fully comply with required post-operative visits associated with HAI chemotherapy Exclusion Criteria: * Presence of extensive or multifocal metastatic extrahepatic or peritoneal disease. Clinical or radiographic evidence of metastatic disease to regional lymph nodes will be allowed, as will limited pulmonary disease at the discretion of the OHSU PI * Prior treatment with floxuridine, oxaliplatin, or irinotecan * Prior treatment with hepatic arterial infusion therapy * Known to have experienced an allergic reaction or other signs of intolerance to implanted devices * Body size that is insufficient to accommodate the physical size of the pump * Diagnosis of sclerosing cholangitis * Diagnosis of hepatic encephalopathy * Clinical evidence of portal hypertension (ascites, gastroesophageal varices, or portal vein thrombosis) or hepatic venous wedge pressures \> 8 mmHg if available * History of multiple abdominal operations that would preclude HAI pump placement * Active infection * Current biliary obstruction requiring placement of endoscopic or transhepatic stents for biliary decompression * Presence of aberrant or replaced hepatic arterial anatomy not amenable to placement of a hepatic arterial infusion pump catheter as judged by the operating surgeon * History of peripheral neuropathy \> grade 1 * Allergies to iodine contrast medium, that cannot be premedicated with steroids per institutional radiology guidelines (e.g., dexamethasone) * Uncontrolled severe coagulation disorders (INR \> 1.5 in patients not on warfarin therapy) * Pregnant or lactating women * History of malignancy other than cholangiocarcinoma within 5 years prior to screening, with the exception of: * Malignancies with a negligible risk of metastasis or death (e.g., 5-year overall survival \[OS\] rate \> 90%), such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, melanoma in situ, localized prostate cancer, ductal carcinoma in situ, or * Stage I uterine cancer or a malignancy whose natural history or treatment has, in the opinion of the principal investigator, the potential to interfere with the safety or efficacy assessment of the intervention under investigation * Life expectancy =\< 12 weeks * Inability to comply with study and/or follow-up procedures * Emotional or psychiatric problems that would preclude successful participation in the hepatic arterial infusion program as judged by the one of the study investigators, and further corroborated by the mandatory interview and assessment with medical oncology social worker * EXCLUSION CRITERIA FOR TREATMENT PERIOD 2 * Participants with radiographic evidence of extrahepatic disease * Evidence of extrahepatic disease found at laparoscopy during open surgical exploration for HAI pump implantation. Participants with extrahepatic disease found at time of laparoscopy or laparotomy will not undergo surgical placement of HAI pump