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

This phase II trial studies the efficacy (the effect on the tumor) and the safety (the effect on the body) of the study drugs when given as a combination in participants with this type of cancer. Another purpose of the study is to see which tumor markers (proteins in the blood that the body produces in response to the cancer) lead to better results in participants treated with the study drugs. Nivolumab and ipilimumab are antibodies, which are human proteins that recognize and attach to a part of the tumor and/or body's immune cells. They work in slightly different ways to activate the immune system and help the body's immune system to work against tumor cells. Nivolumab and ipilimumab are investigational because they are not approved by the FDA to be used for the type of cancer being studied.

PRIMARY OBJECTIVES:

I. To assess median progression-free survival rate (PFSR) as well as PFSR at 6 and 12 months in patients with recurrent or metastatic adenoid cystic carcinoma (ACC) treated with a combination of nivolumab and ipilimumab.

SECONDARY OBJECTIVES:

I. To assess the efficacy of nivolumab and ipilimumab according to response rate (RR), disease control rate (DCR; complete response \[CR\], partial response \[PR\], and stable disease \[SD\] at 6 and 12 months), overall survival (OS) and progression free survival (PFS) using Response Evaluation Criteria in Solid Tumors (RECIST) criteria in patients with recurrent or metastatic ACC.

II. To assess the efficacy of nivolumab and ipilimumab according to overall response rate (ORR), DCR, progression free survival (PFS), and OS in patients with recurrent or metastatic ACC using immune-related response criteria (irRC) criteria.

III. To assess the safety and tolerability profile of nivolumab and ipilimumab therapy in patients with recurrent or metastatic ACC using Common Terminology Criteria for Adverse Events (CTCAE) version 4.03.

TERTIARY OBJECTIVES:

I. Assess safety, tolerability and activity of Nivolumab and Ipilimumab in non-ACC malignant salivary gland tumors (MSGT's) using clinical benefit rate (CBR), ORR, PFS, OS.

II. To assess the predictive value of genomic aberrations observed upon comprehensive genomic profiling of the tumor deoxyribonucleic acid (DNA) derived from archival tumor tissue, if available, or blood from patients with recurrent or metastatic ACC and non-ACC MSGTs.

III. Circulating cell free DNA genomic profiling will also be performed at baseline and during treatment with each imaging to explore the genomic landscape of clonal evolution that may elucidate mechanisms behind response or resistance with immunotherapy in adenoid cystic carcinoma and non-ACC MSGTs.

IV. Correlation between expression of PD-L1 and response to treatment will be explored in all patients enrolled in the study.

V. Correlations between other markers of inflammatory/immune signature will be performed that may include but not be limited to PD-1, OX40, CD73, CD39, T cell immunoglobulin and mucin domain containing protein 3 (TIM3), GITRL, CTLA-4, CD3, CD4, CD8, protein tyrosine phosphatase receptor type C (CD45RO), forkhead box P3 (FOXP3), and granzyme by immunohistochemistry analysis and/or flow cytometry.

OUTLINE:

Patients receive nivolumab intravenously (IV) over 30 minutes on days 1, 15, 29, 43, 57, and 71 of course 1 and on days 1 and 15 of course 2, over 60 minutes on days 29 and 57 of course 2 and on days 1, 29, and 57 of subsequent courses. Patients also receive ipilimumab over 90 minutes on days 1 and 43. Courses repeat every 84 days in the absence of disease progression, unexpected toxicity, or withdrawal of consent.

After completion of study treatment, patients are followed up for 30 days, every 4 weeks for 12 weeks, and then every 12 weeks for up to 2 years.

Eligibility Criteria:
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)
* Patients with history of central nervous system (CNS) metastases are eligible if CNS disease has been stable for at least 6 weeks prior to study registration in the opinion of the investigator and does not require corticosteroids (of any dose) for symptomatic management

  * 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

Exclusion Criteria:

* Patients must not have had chemotherapy or radiotherapy =\< 28 days prior to study registration
* Patients who have not recovered to =\< grade 1 or tolerable grade 2 from adverse events due to agents administered \>= 28 days earlier are not eligible
* Patient must not be a candidate for surgical treatment or radiation
* Patients may not be receiving any other investigational agents =\< 28 days prior to registration
* Patients who have had prior exposure to immune checkpoint inhibitors are not eligible; please contact principal investigator, 312-926-4248 for specific questions on potential interactions

  * NOTE: Immune checkpoint inhibitors working through OX40 are an exception (for example, MEDI6383, MEDI6469, MEDI0562, oxelumab, and PF-04518600) and are permitted \>= 28 days prior to study registration
* Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including chronic prolonged systemic corticosteroids (defined as corticosteroid use of duration one month or greater), should be excluded; these include but are not limited to patients with a history of:

  * Immune related neurologic disease
  * Multiple sclerosis
  * Autoimmune (demyelinating) neuropathy
  * Guillain-Barre syndrome
  * Myasthenia gravis
  * Systemic autoimmune disease such as SLE
  * Connective tissue diseases
  * Scleroderma
  * Inflammatory bowel disease (IBD)
  * Crohn's
  * Ulcerative colitis
  * Patients with a history of toxic epidermal necrolysis (TEN)
  * Stevens-Johnson syndrome
  * Anti-phospholipid syndrome
  * NOTE: Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll
* Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible:

  * Ongoing or active infection (including minor localized infections) requiring oral or IV treatment
  * Symptomatic class 3 or 4 congestive heart failure, defined as a clinical syndrome resulting from any structural or functional cardiac disorder that impairs the ability of the ventricle to fill with or eject blood
  * Unstable angina pectoris
  * Cardiac arrhythmia
  * Psychiatric illness/social situations that would limit compliance with study requirements
  * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints
* Patients should not have any condition requiring systemic treatment with corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days prior to first dose of study drug

  * NOTE: Inhaled or topical steroids and adrenal replacement steroids at any dose are permitted in the absence of active autoimmune disease; a brief (less than 3 weeks) course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by a contact allergen) is permitted
* Female patients who are pregnant or nursing are not eligible
* No other prior malignancy is allowed except for the following:

  * Adequately treated basal cell or squamous cell skin cancer,
  * In situ cervical cancer,
  * Or any other cancer from which the patient has been disease free for at least three years
* Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) is not permitted
* Any known positive test for hepatitis B or hepatitis C virus indicating acute or chronic infection is not permitted
* Patients who received a live, attenuated vaccine =\< 30 days before study registration or are anticipated to require such a live attenuated vaccine are not eligible

  * NOTE: Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine (e.g., FluMist) =\< 30 days prior to study registration or at any time during the study