Testing the Combination of Pevonedistat With Chemotherapy for Bile Duct Cancer of the Liver

Inclusion Criteria: * Patient must be \>= 18 years of age * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Patient must have a life expectancy \>= 12 weeks * Patient must have histologically confirmed intrahepatic cholangiocarcinoma or biphasic hepatocellular carcinoma and cholangiocarcinoma that is metastatic or unresectable and who have progressed on or been intolerant of one prior line of systemic gemcitabine containing chemotherapy regimen. * NOTE: Prior immunotherapy or targeted therapies are allowed and will not be considered a line of therapy unless administered with cytotoxic chemotherapy * Patient must have measurable disease. For patients who have received localized therapy (embolization, chemoembolization, radiofrequency ablation or radiation) are eligible if measurable disease is not within the treatment field or the treated disease has clearly progressed since last localized therapy * Leukocytes \>= 3,000/mcL (obtained within 14 days prior to randomization) * Absolute neutrophil count \>= 1,500/mcL (obtained within 14 days prior to randomization) * Platelets \>= 100,000/mcL (obtained within 14 days prior to randomization) * Total bilirubin =\< institutional upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome may enroll if direct bilirubin =\< 1.5 x ULN of the direct bilirubin (obtained within 14 days prior to randomization) * Hemoglobin \>= 9 g/dL (obtained within 14…