Inclusion Criteria:

          -  Previously treated relapsed and refractory multiple myeloma per International Myeloma
             Working Group consensus criteria (Rajkumar et al., 2011).

          -  Patients must have received at least three prior lines of therapy, including an
             immunomodulatory drug (e.g. lenalidomide, pomalidomide), a proteasome inhibitor (e.g.
             bortezomib, carfilzomib), and anti-CD38 monoclonal antibody (e.g. daratumumab)

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (see Appendix A).

          -  Age ≥ 18 years

          -  All laboratory assessments for eligibility should be performed within 21 days of
             initiation of protocol therapy unless otherwise specified.

          -  Measurable disease of multiple myeloma as defined by at least one of the following
             (IgD and IgA with monoclonal protein < 0.5 g/dL may be permitted after discussion with
             PI):

               -  Serum monoclonal protein ≥ 0.5 g/dL (or quantitative IgA ≥ 1000 mg/dL), or

               -  ≥ 200 mg of monoclonal protein in the urine on 24-hour urine protein
                  electrophoresis, and/or

               -  Serum free light chain ≥ 100 mg/L (10 mg/dL) and abnormal serum free kappa to
                  serum free kappa light chain ratio

          -  ANC ≥ 1000/μL. G-CSF is not permitted within 14 days of screening.

          -  Platelet count ≥ 75,000/µL. Platelet transfusions are not permitted within 7 days of
             screening.

          -  Hemoglobin ≥ 8 g/dL. Red blood cell transfusions are permitted to meet eligibility
             criteria.

          -  Calculated creatinine clearance of ≥ 30 mL/min according to Cockroft-Gault equation.

          -  Adequate hepatic function, as evidenced by each of the following:

               -  Serum aspartate transaminase (ALT) and/or aspartate transaminase (AST) values < 3
                  × the institutional upper limit of normal (ULN).

               -  Serum bilirubin values < 1.5 mg/dL. Patients with elevated bilirubin due to
                  Gilbert's syndrome may be permitted with PI approval.

          -  Able to swallow capsules whole (ixazomib capsules should not be crushed, dissolved or
             broken).

          -  Women of childbearing potential (WOCBP)* must agree to follow instructions for methods
             of contraception for the duration of study treatment with nivolumab and for five
             months after the last dose of study treatment. If they are of childbearing potential,
             agree to practice 2 effective methods of contraception, at the same time, from the
             time of signing the informed consent form through five months after the last dose of
             study drug OR agree to practice true abstinence when it in line with the preferred and
             usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation,
             symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of
             contraception.

             -- Women of child bearing potential are women who are not postmenopausal for at least
             one year and who are not surgically sterile.

          -  Males who are sexually active (even if surgically sterilized, i.e. vasectomy) with
             WOBCP must agree to follow instructions for methods of contraception for the duration
             of study treatment with nivolumab and 7 months after the last dose of study treatment.
             Agree to practice effective barrier contraception during the entire study treatment
             period and through 7 months after the last dose of study drug, or agree to practice
             true abstinence when this is in line with the preferred and usual lifestyle of the
             subject. Periodic abstinence (e.g. calendar, ovulation, symptothermal, post-ovulation
             methods) and withdrawal are not acceptable methods of contraception.

          -  Patient has given voluntary, signed written informed consent before performance of any
             study-related procedure that is not part of standard medical care, with the
             understanding that consent may be withdrawn by the patient at any time without
             prejudice to their future medical care

        Exclusion Criteria:

          -  Prior therapy with ixazomib

          -  Prior therapy with any anti-PD1 antibody (e.g. nivolumab, pembrolizumab) or anti-PDL1
             antibody (e.g. atezolizumab, avelumab, durvalumab)

          -  Participants who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for
             nitrosoureas or mitomycin C) or with monoclonal antibodies 3 weeks of C1D1 or those
             who have not recovered from adverse events due to agents administered more than 2
             weeks earlier. Patients may have received dexamethasone within 2 weeks prior to C1D1.

          -  Participation in other clinical trials, including those with other investigational
             agents, within five half-lives prior to C1D1and throughout the duration of this trial.
             Prior treatment with an investigational agent within five half lives prior to C1D1 may
             be permitted after discussion with the PI.

          -  Concomitant high-dose corticosteroid use except chronic steroids (maximum dose 10
             mg/day prednisone equivalent) if they are being given for disorders other than
             myeloma, e.g. adrenal insufficiency, rheumatoid arthritis, etc.

          -  Female patients who are lactating or have a positive serum pregnancy test during the
             screening period (within 21 days of C1D1).

          -  Prior history of malignancies, other than MM, unless the patient has been free of the
             disease for ≥ 3 years. Exceptions include the following if the patient has undergone
             complete resection:

               -  Basal or squamous cell carcinoma of the skin

               -  Carcinoma in situ of the cervix

               -  Ductal carcinoma in situ of the breast

               -  Incidental histologic finding of prostate cancer (T1a or T1b)

          -  Patients with another malignancy undergoing active treatment with the exception of
             non-melanoma skin cancer or in situ cervical cancer.

          -  Patients with plasma cell leukemia, POEMS syndrome, or amyloidosis are excluded from
             this trial.

          -  HIV infection.

          -  Active hepatitis B infection or active hepatitis C infection. Participants who have
             prior hepatitis C infection and who have received an antiviral treatment and show no
             detectable viral RNA for 6 months prior to screening are eligible.

          -  Peripheral neuropathy ≥ grade 2 despite supportive therapy.

          -  Prior allogeneic stem cell transplant within five years prior to study registration.
             Patients who have had an allogeneic stem cell transplant within five years prior to
             study registration may participate as long as there are no symptoms of graft versus
             host disease.

          -  Patient has a history of significant cardiovascular, neurological, endocrine,
             gastrointestinal, respiratory, or inflammatory illness that could preclude study
             participation, pose an undue medical hazard, or interfere with the interpretation of
             the study results, including, but not limited to, patients with congestive heart
             failure (New York Heart Association [NYHA] Class 3 or 4); unstable angina; cardiac
             arrhythmia; recent (within the preceding 6 months) myocardial infarction or stroke;
             hypertension requiring > 2 medications for adequate control; diabetes mellitus with >
             2 episodes of ketoacidosis in the preceding 12 months; or chronic obstructive
             pulmonary disease (COPD) requiring > 2 hospitalizations in the preceding 12 months.

        3.2.15 Autoimmune disease: patients with a history of inflammatory bowel disease, including
        ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with
        a history of symptomatic disease (e.g., rheumatoid arthritis, systemic progressive
        sclerosis [scleroderma], systemic lupus erythematosus, autoimmune pneumonitis, autoimmune
        vasculitis (e.g., Wegener's granulomatosis) and motor neuropathy considered of autoimmune
        origin (e.g. Guillain-Barré syndrome and myasthenia gravis). Patients 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 with history of interstitial lung disease and/or pneumonitis, or pulmonary
             hypertension.

          -  Major surgery within 14 days prior to study registration.

          -  Central nervous system involvement.

          -  Infection requiring systemic antibiotic therapy or other serious infection within 14
             days prior to study registration

          -  Systemic treatment with strong CYP3A inducers (rifampin, rifapentine, rifabutin,
             carbamazepine, phenytoin, phenobarbital), or use of St. John's wort within 14 days
             prior to C1D1.

          -  Receipt of a live or attenuated vaccine within 30 days of C1D1.

          -  Any serious medical of psychiatric illness that could, in the investigator's opinion,
             potentially interfere with the completion of treatment according to this protocol.

          -  Known allergy to any study medications, their analogs, or excipients in the various
             formulations of any agent.