Mezigdomide (CC-92480) Post Idecabtagene Vicleucel in Treating Patients With Relapsed Multiple Myeloma

This phase I trial studies the safety, side effects, best dose and effectiveness of mezigdomide (CC-92480) when given after idecabtagene vicleucel (Abecma chimeric antigen receptor \[CAR\] T-cell therapy) in patients with multiple myeloma that has come back after a period of improvement (relapsed). CC-92480 works by binding to a protein called CRBN that triggers the breakdown of proteins: Ikaros and Aiolos, leading to cell death in multiple myeloma cells. Giving mezigdomide after Abecma CAR T cell therapy may extending the amount of time that the CAR T cells persist in the body in patients with relapsed multiple myeloma.

PRIMARY OBJECTIVE:

I. To evaluate the safety and tolerability of mezigdomide (CC-92480) given post idecabtagene vicleucel when administered as a continued therapy.

SECONDARY OBJECTIVES:

I. To evaluate the anti-tumor activity of mezigdomide (CC-92480) when administered post idecabtagene vicleucel.

II. To determine the persistence of CAR T cells at day 90 (D90), day 180 (D180), and day 365 (D365) after start of mezigdomide (CC-92480) therapy.

EXPLORATORY OBJECTIVES:

I. To assess levels of serum BCMA monthly at day 1 of every cycle. II. To assess the effects of mezigdomide (CC-92480) on non-cancer immune cells in the peripheral blood and bone marrow samples.

OUTLINE: This is a dose-escalation study of mezigdomide.

Starting between 30 and 90 days after infusion of idecabtagene vicleucel, patients receive mezigdomide orally (PO) on days 1-21 or days 1-14 of each cycle. Treatment repeats every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo positron emission tomography (PET)/computed tomography (CT) during screening. Patients also undergo bone marrow aspiration and blood sample collection throughout the study.

After completion of study treatment, patients are followed up at 30 days, every 3 months within 1 year of start of treatment, and then every 6 months until progression or for up to 2 years.

Eligibility Criteria:
Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative.

  * Assent, when appropriate, will be obtained per institutional guidelines
* Age: \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) =\< 2
* Diagnosis of multiple myeloma
* Subject must have received at least 4 prior lines of therapy, including an immunomodulatory agent, a proteasome inhibitor, and an anti-CD38 antibody
* Receipt of commercially available idecabtagene vicleucel (Abecma) according to FDA approved US Prescribing Information. Note: Patients who received non-conforming Abecma who were originally prescribed Abecma according to the FDA approved label may be considered for inclusion per the investigators discretion. Subject must be between day 30 and day 90 post receipt of idecabtagene vicleucel
* Subject must have experienced at least a stable disease in response to idecabtagene vicleucel
* Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 to prior anti-cancer therapy, including idecabtagene vicleucel
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3 without the use of filgrastim in the previous 3 days (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated)

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Platelets \>= 75,000/mm\^3 without platelet transfusion in the previous 3 days. (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated)

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Total bilirubin =\< 1.5 X upper limit of normal (ULN) (unless has known Gilbert's disease) (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated).

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Aspartate aminotransferase (AST) =\< 3 x ULN (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated).

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Alanine transaminase (ALT) =\< 3 x ULN (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated).

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Alkaline phosphatase =\< 5 x ULN (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated)
* Creatinine clearance of \>= 50 mL/min per 24 hour urine test or the Cockcroft-Gault formula (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated).

  * Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Oxygen saturation \> 92% on room air (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated)
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required (To be performed within 14 days prior to day 1 of protocol therapy unless otherwise stated)
* Agreement by females of childbearing potential and males to follow the guidelines of the mezigdomide (CC-92480) pregnancy prevention plan

Exclusion Criteria:

* Prior exposure to mezigdomide (CC-92480)
* Current or planned use of other therapies other than mezigdomide (CC-92480)
* Patients who are currently receiving or likely to require systemic immunosuppressive therapy. Physiologic replacement of steroids (=\< 5.0 mg/day prednisone or equivalent) is allowed
* Concomitant use of CYP3A4/5 inhibitors and inducers
* Concomitant use of proton pump inhibitors
* Evidence of relapse as evaluated by the treating physician or study investigator
* Active central nervous system involvement
* Ongoing toxicities associated with cytokine release syndrome (CRS) or Immune effector cell-associated neurotoxicity syndrome (ICANS) from CAR T cell therapy
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent
* Coronavirus disease 2019 (COVID-19) positive, as assessed by a polymerase chain reaction (PCR) test or active uncontrolled infections (defined as active antibiotic use within 7 days of starting the investigational drug)
* If human immunodeficiency virus (HIV) positive: CD4+ T cell count \< 200
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)