Retifanlimab (INCMGA00012) and Telotristat Ethyl for the Treatment of Advanced Neuroendocrine Tumors and Carcinoid Syndrome

Inclusion Criteria: * Grade 1, 2, or 3 (or described as low grade, intermediate grade, well differentiated, or moderately differentiated) neuroendocrine tumor, according to reviewing pathologist or documented interpretation of report by the investigator * Progressive disease over the preceding 12 months * Prior therapy with any number of anticancer therapies, but a somatostatin analogue (such as octreotide, lanreotide, or pasireotide) must be one of the prior therapies * Carcinoid syndrome, as documented by the investigator * Patients using a somatostatin analogue for symptom control must be on stable doses for 56 days prior to enrollment * Signed informed consent form * Age \>= 18 years * Ability to comply with the study protocol, in the investigator's judgment * Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 * Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Absolute neutrophil count \>= 1,500/mm\^3 without granulocyte colony-stimulating factor support (obtained within 28 days prior to initiation of study treatment) * Lymphocyte count \>= 500/mm\^3 (obtained within 28 days prior to initiation of study treatment) * Platelet count \>= 100,000/mm\^3 without transfusion (obtained within 28 days prior to initiation of study treatment) * White blood cell count \>= 2,500/mm\^3 (obtained within 28 days prior to initiation of study treatment) * Hemoglobin \>= 9.0 g/dL (obtained within 28 days prior to initiation of study treatment) * Patients may be transfused to meet this criterion * Aspartate transaminase (AST), alanine transaminase (ALT), and alkaline phosphatase =\< 2.5 x upper limit of normal (ULN) (obtained within 28 days prior to initiation of study treatment), with the following exceptions: * Patients with documented liver metastases: AST and ALT =\< 5 x ULN * Patients with documented liver or bone metastases: alkaline phosphatase =\< 5 x ULN * Serum bilirubin =\< 1.5 x ULN (obtained within 28 days prior to initiation of study treatment) with the following exception: * Patients with known Gilbert disease: serum bilirubin level =\< 3 x ULN * Serum creatinine =\< 1.5 x ULN (obtained within 28 days prior to initiation of study treatment) * Serum albumin \>= 2.5 g/dL (obtained within 28 days prior to initiation of study treatment) * For patients not receiving therapeutic anticoagulation: international normalized ratio (INR) or activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (obtained within 28 days prior to initiation of study treatment) * For patients receiving therapeutic anticoagulation: stable anticoagulant regimen * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use a barrier contraceptive method with a failure rate of \< 1% per year during the treatment period and for 6 months after the last dose of study treatment * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for 6 months after the last dose of study treatment * A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus) * Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception Exclusion Criteria: * Grade 3, poorly differentiated neuroendocrine carcinoma * Large cell or small cell histology * Treatment for the studied cancer within 28 days prior to initiation of study treatment * Treatment with investigational therapy within 28 days prior to initiation of study treatment * Palliative radiation therapy administered within 1 week of first dose of study treatment or radiation therapy in the thoracic region that is \> 30 Gy within 6 months of the first dose of study treatment. Note: Participants must have recovered from all radiation-related toxicities, not require corticosteroids for this purpose, and not have had radiation pneumonitis * Toxicity of prior therapy that has not recovered to =\< grade 1 or baseline (with the exception of any grade of alopecia and anemia not requiring transfusion support) * Known hypersensitivity to another monoclonal antibody that cannot be controlled with standard measures (e.g., antihistamines and corticosteroids) * Known allergy or hypersensitivity to any component of the INCMGA00012 formulation * Known allergy or hypersensitivity to any component of the telotristat formulation * Active autoimmune disease requiring systemic immunosuppression in excess of physiologic maintenance doses of corticosteroids (\> 10 mg/day of prednisone or equivalent) * Physiologic corticosteroid replacement therapy at doses \> 10 mg/day of prednisone or equivalent for adrenal or pituitary insufficiency and in the absence of active autoimmune disease is permitted * Participants with asthma that requires intermittent use of bronchodilators, inhaled steroids, or local steroid injections may participate * Brief courses of corticosteroids for prophylaxis (e.g., contrast dye allergy) or study treatment-related standard premedication are permitted * Participants using topical, ocular, intra-articular, or intranasal steroids (with minimal systemic absorption) may participate * Prior allogeneic stem cell or solid organ transplantation * Evidence of interstitial lung disease, history of interstitial lung disease, or active, noninfectious pneumonitis * Positive human immunodeficiency virus (HIV) test at screening with CD4+ T-cell count \< 350 cells/mcL * Known HIV infection and opportunistic infection within the past 12 months * Active hepatitis B virus (HBV) infection (chronic or acute), defined as having a positive hepatitis B surface antigen (HBsAg) test at screening * Patients with a past or resolved HBV infection, defined as having a negative HBsAg test and a positive total hepatitis B core antibody (HBcAb) test and negative HBV deoxyribonucleic acid (DNA) test at screening, are eligible for the study * Active hepatitis C virus (HCV) infection, defined as having a positive HCV antibody test followed by a positive HCV ribonucleic acid (RNA) test at screening * The HCV RNA test will be performed only for patients who have a positive HCV antibody test * Known diagnosis of active tuberculosis * Treatment with therapeutic oral or IV antibiotics within 7 days prior to initiation of study treatment * Patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study * Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during the course of the study, or up to 5 months following the anticipated last dose of INCMGA00012 * Malignancies other than the disease under study within 3 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per standard-of-care management (e.g., chronic lymphocytic leukemia Rai stage 0) * Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of an investigational drug, may affect the interpretation of the results, or may render the patient at high risk from treatment complications * Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, and anti-PD-L1 therapeutic antibodies * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2) within 4 weeks or five half-lives of the drug (whichever is longer) prior to initiation of study treatment * Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF-alpha agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during the course of the study, with the following exceptions: * Patients who received low-dose immunosuppressant medication are eligible for the study * Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study * Pregnant or breastfeeding, or intending to become pregnant during the study * Women of childbearing potential must have a negative serum pregnancy test result within 14 days prior to initiation of study treatment