Similar to another study.

This study has 2 parts: a Dose Escalation Part and a Dose Expansion Part.

The goal of the Dose Escalation Part of this clinical research study is to find the highest tolerable dose of nivolumab in combination with ipilimumab and the standard of care (lenalidomide and dexamethasone) that can be given to patients with multiple myeloma (MM).

The goal of the Dose Expansion Part of this clinical research study is to continue to study the safety of the highest tolerable dose found in Phase 1 of the study.

Study Groups:

If participant is found to be eligible to take part in this study, participant will be assigned to a study group based on when participant joins this study. Up to 2 groups of up to 6 participants each will be enrolled in the Dose Escalation Part of the study, and up to 24 participants will be enrolled in the Dose Expansion Part.

If participant is enrolled in the Dose Escalation Part, the dose of nivolumab participant receives will depend on when participant joins this study. The first group of participants will receive the lowest dose level of nivolumab. A second group will then receive a higher dose of nivolumab than the group before it, if no intolerable side effects were seen.

If participant is enrolled in the Dose Expansion Part, participant will receive nivolumab at the highest dose that was tolerated in the Dose Escalation Part.

All participants will receive the same dose levels of ipilimumab, dexamethasone, and lenalidomide.

Study Drug Administration:

The first 4 study cycles will be 21 days long, and all remaining cycles will be 28 days long.

On Day 1 of Cycles 1-4, participant will receive nivolumab by vein over 60 minutes. Thirty (30) minutes after participant receives nivolumab, participant will receive ipilimumab by vein over 90 minutes. On Days 1 and 15 of Cycles 5 and beyond, participant will receive nivolumab by vein over 60 minutes.

Participant will take tablets of lenalidomide on Days 1-14 of Cycles 1-4 and on Days 1-21 of Cycles 5 and beyond. Participant will take tablets of dexamethasone on Days 1, 8, and 15 of Cycles 1-4, and on Days 1, 8, 15, and 22 of Cycles 5 and beyond.

Study Visits:

On Day 1 of Cycles 1- 4 (+/- 7 days):

• Participant will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine tests, biomarker testing, and to check the status of the disease. If participant can become pregnant, this routine testing will also include a pregnancy test.
• Urine will be collected over 24 hours for routine tests and to check the status of the disease.
• During Cycle 3 only, participant will have 2 bone marrow biopsies/aspirations to check the status of the disease and for biomarker testing, including genetic biomarkers.
• During Cycle 3 only, urine will be collected for biomarker testing.

At the end of Cycle 4, participant will have an ECHO and pulmonary function test to check the status of participant's lungs and heart.

On Day 1 of Cycles 5 and beyond:

• Participant will have a physical exam.
• Blood (about 2 tablespoons) and urine will be collected for routine tests and to check the status of the disease. If participant can become pregnant, this routine testing will also include a pregnancy test.
• Urine will be collected over 24 hours for routine tests and to check the status of the disease.
• Some participants will have a stem cell transplant after Cycle 4. If participant does not have a stem cell transplant, blood (about 1 tablespoon) will be drawn for tests of the immune system every cycle. If participant does have a stem cell transplant, this will only be done every 3 cycles.
• If participant does not have a stem cell transplant, on Day 1 of Cycles 5 and every 3 cycles after that, urine will be collected for biomarker testing.

On Day 15 of Cycles 5 and beyond, blood (about 1 tablespoon) will be drawn for routine tests.

If at any point participant does have a stem cell transplant, participant will have 2 bone marrow biopsies or aspirations to check the status of the disease and for biomarker testing after the transplant.

End-of-Treatment Visits:

When participant stops taking the study drug:

• Blood (about 1-2 tablespoons) and urine will be collected for routine tests, to check the status of the disease, and to learn how the study drugs work in participant's body. If participant can become pregnant, part of this blood will be used for a pregnancy test.
• Participant will have 2 bone marrow biopsies/aspirations to check the status of the disease and for biomarker testing, including genetic biomarkers.

If at any point the disease gets worse:

• Blood (about 2 tablespoons) and urine will be collected for routine tests and to check the status of the disease.
• Urine will be collected over 24 hours for routine tests and to check the status of the disease.
• Participant will have a bone survey to check the status of the disease.
• Participant will have a bone marrow biopsy or aspiration to check the status of the disease and for biomarker testing, including genetic biomarkers.
• Blood (about 3 teaspoons) will be drawn for genetic testing to learn if there is a relationship between participant's genes and the disease

Follow-Up:

If the doctor thinks it is needed, participant may have the following tests. The schedule for these tests will depend on what participant's doctor thinks is in participant's best interest.

• Blood (about 2 tablespoons) and urine will be collected for routine tests and to check the status of the disease. If participant can become pregnant, this routine testing will also include a pregnancy test.
• Urine will be collected over 24 hours for routine tests and to check the status of the disease.
• Participant will have bone marrow biopsies or aspirations to check the status of the disease and for biomarker testing, including genetic biomarkers.
• Participant will have a bone survey to check the status of the disease.

This is an investigational study. Nivolumab and ipilimumab are FDA approved for the treatment of certain types of melanoma. Their use in patients with MM is investigational. Lenalidomide in combination with dexamethasone is FDA approved for the treatment for multiple myeloma. The study doctor can explain how the study drugs are designed to work.

Up to 36 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patients must have been previously diagnosed with histologically or cytologically confirmed multiple myeloma
2. Patients must have measurable disease, as defined by at least one of the following: * Serum monoclonal protein level >/=0.5 g/dL for IgG, IgA, or IgM disease * Monoclonal protein or total serum IgD >/=0.5 g/dL for IgD disease * Urinary M-protein excretion of >/=200 mg over a 24-hour period * Involved free light chain level >/=10 mg/dL, along with an abnormal free light chain ratio
3. Patients must be age 18 or older, and must be willing and able to provide voluntary written informed consent, with the understanding that consent may be withdrawn by the subject at any time without prejudice to their future medical care
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 Karnofsky >/=60%.
5. Patients must have evidence of adequate bone marrow reserves, as defined by the following: * Absolute neutrophil count (ANC) >/= 1,000 cells/mm^3 * Hemoglobin >/= 9 g/dL, independent of blood transfusions * Platelet counts of >/= 100,000 cells/mm^3 for patients who have bone marrow plasmacytosis of <50%, or >/= 50,000 cells/mm^3 for patients who have bone marrow plasmacytosis of >/= 50%
6. Patients must have evidence of adequate hepatic function, as defined by the following: * Total bilirubin </= 1.5 times the upper limit of the institutional normal values (except in subjects with Gilbert Syndrome, who can have a total bilirubin < 3.0 mg/dL) * Total AST (SGOT) and ALT (SGPT) </= 3 times the upper limit of the institutional normal values
7. Patients must have evidence of adequate renal function, as defined by the following: * Serum creatinine within the institutional normal limits, OR if the creatinine is elevated * Creatinine clearance (CrCl) >/= 40 mL/min., as measured by a 24-hour urine collection, or estimated by the Cockcroft and Gault formula: Female CrCl = (140 - age in years) x weight in kg x 0.85 / 72 x serum creatinine in mg/dL Male CrCl = (140 - age in years) x weight in kg x 1.00 / 72 x serum creatinine in mg/dL
8. Patients must have evidence of adequate cardiac function, as defined by the following: * Absence of New York Heart Association (NYHA) class II, III, or IV congestive heart failure * Absence of uncontrolled angina or hypertension * Absence of myocardial infarction in the previous 6 months * Absence of clinically significant bradycardia, or other uncontrolled cardiac arrhythmia defined as grade 3 or 4 according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0
9. Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy for 23 weeks (30 days plus the time required for nivolumab/ipilimumab to undergo five half-lives) after the last dose of investigational drug. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab/ipilimumab. Additionally WOCBP must use adequate methods of contraception for the duration of the study consistent with the standard requirements for lenalidomide.
10. WOCBP is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL.
11. Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving nivolumab/ipilimumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product. Women who are not of childbearing potential (i.e. who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception)
12. Patients must be newly diagnosed and must not have received prior treatment directed to multiple myeloma.

Exclusion Criteria:

1. Patients who have known central nervous system involvement with multiple myeloma will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
2. Patients with a known history of allergic reactions attributed to any compounds of similar chemical or biologic composition to be used on this study.
3. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring intravenous antibiotics, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements, in the opinion of the Principal Investigator.
4. Pregnant or lactating women.
5. Patients with known active hepatitis A, B, and/or C infection are excluded. This is due to the difficulty that would be faced in assessing the attribution of any events of hepatic toxicity while on therapy.
6. Ongoing graft-versus-host (GVHD) due to prior allogeneic hematopoietic stem cell transplantation. Patients with prior history of acute GVHD or extensive chronic GVHD requiring a minimum of 6 months or longer treatment since allogeneic hematopoietic stem cell transplantation are also excluded.
7. Patients should be excluded if they have an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have 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.
8. Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Additionally, patients will be excluded if they have required therapy for control of GVHD within 4 weeks of study treatment.
9. Patients should be excluded if they have had prior systemic treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways.
10. Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).