This phase II trial studies how well gemcitabine hydrochloride, cisplatin, and nab-paclitaxel (paclitaxel albumin-stabilized nanoparticle formulation) work in treating patients with biliary cancers (which includes the gallbladder and bile ducts inside and outside the liver) that have spread to other places in the body and usually cannot be cured or controlled with treatment. Drugs used in chemotherapy, such as gemcitabine hydrochloride, cisplatin, and paclitaxel albumin-stabilized nanoparticle formulation, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving more than one drug (combination chemotherapy) may kill more tumor cells.

PRIMARY OBJECTIVES:

I. Determine the progression-free survival (PFS) of gemcitabine hydrochloride (gemcitabine), cisplatin, and nab-paclitaxel in advanced, untreated biliary cancers (intrahepatic cholangiocarcinomas, extrahepatic cholangiocarcinomas, and gallbladder cancers).

SECONDARY OBJECTIVES:

I. Determine the response rate (RR) and disease control rate (partial response + complete response + stable disease) of gemcitabine, cisplatin, and nab-paclitaxel in advanced biliary cancers.

II. Determine overall survival (OS) of gemcitabine, cisplatin, and nab-paclitaxel in advanced biliary cancers.

III. Evaluate the toxicity of gemcitabine, cisplatin, and nab-paclitaxel in advanced biliary cancers.

EXPLORATORY OBJECTIVES:

I. Correlate the carbohydrate antigen (CA) 19-9 response (defined as >50% decrease from baseline) with tumor response, PFS and OS.

II. Assess ribonucleotide reductase subunit MI (RRMI), excision repair cross-complementation group 1 (ERCC1) pre-treatment status and correlate with tumor response, PFS and OS on an exploratory basis.

III. Collect optional blood and tissue at the start of treatment and at progression to explore mechanisms of resistance.

OUTLINE:

Patients receive paclitaxel albumin-stabilized nanoparticle formulation intravenously (IV) over 30 minutes, cisplatin IV over 60 minutes, and gemcitabine hydrochloride IV over 30 minutes on days 1 and 8. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days and then every 3 months thereafter.

Inclusion Criteria:

• Patient must have histologically or cytologically confirmed intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, or gallbladder cancer or may undergo a repeat biopsy for histologic confirmation if pre-existing biopsy is not sufficient for diagnosis
• Metastatic or unresectable disease documented on diagnostic imaging studies
• May not have received prior chemotherapy; if patient has received prior adjuvant therapy, must be > 6 months from treatment
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
• Absolute neutrophil count (ANC) >= 1,500 cells/mm^3
• Platelets >= 100,000/ul
• Hemoglobin > 9.0 g/dL
• Total bilirubin =< 1.5 mg/dL (in patients with known Gilbert's syndrome direct bilirubin =< 1.5 x upper limit of normal [ULN] will be used as organ function criteria, instead of total bilirubin)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) = < 5 x ULN
• Creatinine =< 1.5 gm/dL
• Negative serum or urine pregnancy test in women with childbearing potential (WOCBP) defined as not post-menopausal for 12 months or no previous surgical sterilization, within one week prior to initiation of treatment; WOCBP must be using an adequate method of contraception to avoid pregnancy throughout the study and for up to 12 weeks after the last dose of study drug to minimize the risk of pregnancy
• A male subject of fathering potential must use an adequate method of contraception to avoid conception throughout the study and for up to 12 weeks after the last dose of study drug to minimize the risk of pregnancy; if the partner is pregnant or breastfeeding, the subject must use a condom
• Patients must sign an informed consent and authorization indicating that they are aware of the investigational nature of this study and the known risks involved

Exclusion Criteria:

• Peripheral neuropathy of grade 2 or greater by Common Terminology Criteria for Adverse Events (CTCAE) 4.0; in CTCAE version 4.0 grade 2 sensory neuropathy is defined as "moderate symptoms; limiting instrumental activities of daily living (ADLs)"
• Concurrent severe and/or uncontrolled medical conditions which could compromise participation in the study such as unstable angina, myocardial infarction within 6 months, unstable symptomatic arrhythmia, uncontrolled diabetes, serious active or uncontrolled infection
• Pregnancy (positive pregnancy test) or lactation
• Known central nervous system (CNS) disease, except for treated brain metastasis; treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing requirement for dexamethasone, as ascertained by clinical examination and brain imaging (magnetic resonance imaging [MRI] or computed tomography [CT]) during the screening period; anticonvulsants (stable dose) are allowed; treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; Gamma Knife, linear accelerator [LINAC], or equivalent) or a combination as deemed appropriate by the treating physician; patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 will be excluded