An Open-Label Phase II Study of Nivolumab or Nivolumab/Ipilimumab in Adult Participants With Progessive/ Recurrent Meningioma

Inclusion Criteria: * Have histologically confirmed WHO grade I, II or III meningioma that is progressive or recurrent. Metastatic meningiomas are allowed. Participants with grade I tumors must have failed radiation therapy. * Prior therapy: * There is no limit on the number of prior surgeries, radiation therapy, radiosurgery treatments or systemically administered therapeutic agents. * Patients may have been treated with standard external beam radiation or radiosurgery in any combination, however, an interval of ≥ 12 weeks (84 days) must have elapsed from the completion of the radiation therapy to start of study therapy unless there is histopathologic confirmation of recurrent tumor or there is new enhancing tumor outside the radiation field (beyond the high dose region or the 80% isodose line). * In addition, there must be subsequent evidence of tumor progression after completion of radiation therapy (grade I tumors only) * An interval of ≥ 28 days and full recovery (no ongoing safety issues) from surgical resection * An interval of ≥ 7 days from stereotactic biopsy; * For prior systemic agents, participants must be at least 4 weeks (or 5 half-lives, whichever is shorter) from other prior cytotoxic chemotherapy (6 weeks from nitrosoureas) or biologic therapies. * Participants must have recovered to grade ≤ 1 or pretreatment baseline from clinically significant adverse events related to prior therapy (exclusions include but are not limited to alopecia, laboratory values listed per inclusion criteria and lymphopenia); * Be 18 years of age on day of signing informed consent. * Have a Karnofsky performance status (KPS) ≥ 70 (Appendix A). * Participants must demonstrate adequate organ and marrow function as defined below (all screening labs to be performed within 14 days of treatment initiation): * White blood cell (WBC) ≥ 2000/mm3 * Absolute neutrophil count (ANC) ≥ 1,000/mm3 * Platelet count ≥ 100,000/mm3 * Hemoglobin ≥ 9 gm/dl * AST(SGOT)/ALT(SGPT) ≤ 3 x laboratory upper limit of normal (ULN) * Serum creatinine ≤ 1.5 X ULN OR * creatinine clearance (meas or calc) ≥ 60 mL/min for participants with creatinine levels \> 1.5 X ULN * (GFR can be used in place of creatinine or creatinine clearance) * Total serum bilirubin ≤ 1.5 X ULN * (except participants with Gilbert's Syndrome, who can have a total bili \< 5 X ULN) * Resting baseline oxygen saturation ≥ 92% at rest by pulse oximetry * MRI (or CT if MRI contraindicated) within 14 days prior to start of study drug. Corticosteroid dose must be stable or decreasing for at least 5 days prior to the scan. If steroids are added or the steroid dose is increased between the date of the screening MRI or CT scan and the start of treatment, a new baseline MRI or CT is required. * Ability to understand and the willingness to comply with scheduled visits, treatment schedule, laboratory testing, and other requirements of the study, including disease assessment by MRI (or CT), as confirmed by signing a written informed consent document. * For cohort 2, patients must be a candidate for external beam radiotherapy including either conventional fractionated conformal dosing or stereotactic radiosurgical boost dosing (participants may enroll if they are receiving radiotherapy or have completed it within 8 weeks of starting immunotherapy); * For cohort 2 patients who are undergoing fractionated conformal re-irradiation to a tumor site that has been previously irradiated, an interval of at least 6 months must have passed since they completed their prior irradiation to be eligible unless the current course of radiation is targeting a new area of tumor growth outside the 80% isodose line of the original radiation field as determined by the treating investigator. * The effects of nivolumab on the developing human fetus are unknown. For this reason: * Women of childbearing potential (WOCPB; defined in Section 3.4) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours of starting study therapy; * Women must not be breastfeeding; * WOCPB must agree to follow instructions for method(s) of contraception from the time of enrollment for the duration of treatment with study therapy plus 5 months after the last dose of Nivolumab. * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Men who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug plus 7 months after the last dose of Nivolumab. * Investigators shall counsel WOCBP and male subjects who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy Investigators shall advise WOCBP and male subjects who are sexually active with WOCBP on the use of highly effective methods of contraception. Highly effective methods of contraception have a failure rate of \< 1% per year when used consistently and correctly. * At a minimum, subjects must agree to the use of two methods of contraception, with one method being highly effective and the other method being either highly effective or less effective as listed below: * HIGHLY EFFECTIVE METHODS OF CONTRACEPTION * Male condoms with spermicide * Hormonal methods of contraception including combined oral contraceptive pills, vaginal ring, injectables, implants, and intrauterine devices (IUDs) such as Mirena by WOCBP subjects or male subject's WOCBP partner. Female partners of male subjects participating in the study may use hormone based contraceptives as one of the acceptable methods of contraception since they will not be receiving study drug * Progestogen only hormonal contraception associated with inhibition of ovulation * Intrauterine hormone-releasing system (IUS) * Nonhormonal IUDs, such as ParaGard * Tubal ligation * Vasectomy * Complete Abstinence - Complete abstinence is defined as complete avoidance of heterosexual intercourse and is an acceptable form of contraception for all study drugs. Subjects who choose complete abstinence are not required to use a second method of contraception, but female subjects must continue to have pregnancy tests. Acceptable alternate methods of highly effective contraception must be discussed in the event that the subject chooses to forego complete abstinence. * LESS EFFECTIVE METHODS OF CONTRACEPTION * Diaphragm with spermicide * Cervical cap with spermicide * Vaginal sponge * Male Condom without spermicide * Progestin only pills by WOCBP subjects or male subject's WOCBP partner * Female Condom - A male and female condom must not be used together * UNACCEPTABLE METHODS OF CONTRACEPTION * Periodic abstinence (calendar, symptothermal, post-ovulation methods) * Withdrawal (coitus interruptus) * Spermicide only * Lactation amenorrhea method (LAM) * NOTE: Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements. However, WOCBP participants must still undergo pregnancy testing as described. Exclusion Criteria: * Current or planned participation in a study of an investigational agent or using an investigational device. * Tumors that are primarily localized to the brainstem or spinal cord; * Evidence of intratumoral or peritumoral hemorrhage on baseline MRI scan other than those that are grade ≤ 1 and either post-operative or stable on at least 2 consecutive MRI scans; * Prior Therapy: * Prior treatment with systemic immunosuppressive treatments, aside from systemic dexamethasone therapy for cerebral edema, such as methotrexate, chloroquine, azathioprine, etc. within 3 months of start of study therapy; * Prior treatment with interstitial brachytherapy within 6 months of start of study therapy; * All patients: Previous treatment with PD-1 or PD-L1 directed therapy; * Cohort 2 patients: Previous treatment with CTLA-4 directed therapy; * Surgical procedure (including open biopsy, surgical resection, wound revision, or any other major surgery involving entry into a body cavity) or significant traumatic injury within 28 days prior to first study treatment, or anticipation of need for major surgical procedure during the course of the study; * Minor surgical procedure (eg, stereotactic biopsy within 7 days of first study treatment; placement of a vascular access device within 2 days of first study treatment); * Other Meds: * Participants who are receiving any other investigational agents. * Immunosuppressive medications / steroids: * Subject must not require high dose systemic corticosteroids defined as dexamethasone \> 4 mg/day or bioequivalent for at least 3 consecutive days within 2 weeks prior to Day 1of study therapy; * Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Subjects are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). * Physiologic replacement doses of systemic corticosteroids are permitted, even if \> 10 mg/day prednisone equivalents. * A brief course of corticosteroids for prophylaxis (eg, contrast dye allergy) or for treatment of non-autoimmune conditions (eg, delayed-type hypersensitivity reaction caused by contact allergen) is permitted. * Has received a live vaccine within 30 days prior to the first dose of study drug; seasonal influenza vaccination is permitted excluding the nasal spray formulation; * No concurrent treatment on another clinical trial. Supportive care trials or non- treatment trials, e.g. quality of life, are allowed; * Concomitant Medical Illnesses: Uncontrolled intercurrent illness, including-but not limited to: * Known additional malignancy that is progressing or requires active treatment within 3 years of start of study drug. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy; * Has evidence of interstitial lung disease or active, non-infectious pneumonitis; * Any serious or uncontrolled medical disorder that, in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results examples include but are not limited to symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/social situations that would limit compliance with study requirements; * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo, type 1 diabetes mellitus, residual hypothyroidism due to autoimmune condition requiring hormone replacement, psoriasis not requiring systemic treatment, conditions not expected to recur in the absence of an external trigger or resolved childhood asthma/atopy would be exceptions to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjorgen's syndrome will not be excluded from the study; * Has an active infection requiring intravenous therapy; * Positive test for hepatitis B virus surface antigen (HBV sAg) or detectable hepatitis C virus ribonucleic acid (HCV RNA) indicating acute or chronic infection * Medical History: * History of intracranial abscess within 6 months prior to start of study therapy; * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS); * NOTE: HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Nivolumab. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * History of allergy to study drug components * History of severe hypersensitivity reaction to any monoclonal antibody; * Prisoners or participants who are involuntarily incarcerated; * Pregnant women are excluded from this study because Nivolumab is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Nivolumab, breastfeeding should be discontinued if the mother is treated Nivolumab.