Nivolumab and Ipilimumab in Treating Patients With Metastatic/Recurrent ACC of All Sites and Non-ACC Salivary Gland Cancer

Inclusion Criteria

• •Patients must have histologically or cytologically confirmed metastatic/recurrent adenoid cystic carcinoma (ACC) or non-adenoid cystic carcinomas (non-ACC) of major or minor salivary glands
• •Patients must have evidence of disease progression and cannot be a candidate for surgical treatment
• •* NOTE: Disease progression is defined as one of the following occurring within the 6 months prior to study entry:
• •* At least a 20% increase in radiologically or clinically measurable lesions
• •* Appearance of any new lesions or
• •* Symptomatic and/or deterioration in clinical status
• •Patients must have received at least one prior line of systemic therapy
• •* NOTE: There is no limit to the number of prior therapies for stage IV disease
• •* NOTE: Patients should not be a candidate for surgical treatment
• •Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension in accordance with RECIST criteria v1.1
• •Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) status of 0-2
• •* NOTE: ECOG performance status 3 will be allowed only if thought to be directly secondary to adenoid cystic carcinoma disease by treating physician
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: leukocytes \>= 2,000/mcL
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: absolute neutrophil count \>= 1,500/mcL, regardless of transfusion or growth factor support
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: platelets \>= 100,000/mcl, regardless of transfusion or growth factor support
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: total bilirubin total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (except patients with Gilbert syndrome or liver metastasis, who can have total bilirubin \< 3.0 x ULN)
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (ULN) (or =\< 5 times ULN in case of liver metastasis)
• •Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined by: serum creatinine of \< 3.0 X ULN (upper limit of normal) or creatinine clearance \> 30 mL/minute (using Cockcroft/Gault formula)
• •* NOTE: Only patients with a known history or indication of CNS disease are required to have CNS imaging prior to study entry
• •Females of childbearing potential (FOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 72 hours of registration
• •* NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:
• •* Has not undergone a hysterectomy or bilateral oophorectomy
• •* Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months)
• •FOCBP and men who are sexually active with FOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment and the designated post-treatment period
• •Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study