Testing the Addition of Iberdomide to Therapy in People With Neuroblastoma That Has Come Back, Not Responded to Treatment, or Gotten Worse

Inclusion Criteria: * Patients must be ≥ 1 year of age and ≤ 30 years of age at the time of study enrollment * Patients must have had histologic verification of neuroblastoma or ganglioneuroblastoma or demonstration of neuroblastoma cells in the bone marrow with elevated urinary catecholamines (i.e. \> 2 x upper limit of normal \[ULN\]), at the time of initial diagnosis * Progressive/relapsed or refractory (defined as persistent disease with overall response no better than minor response \[MR\] to prior therapy per revised International Neuroblastoma Response Criteria \[INRC\]) neuroblastoma based on the revised INRC * Patients must meet ONE of the following criteria: * Primary refractory disease * Primary refractory disease following chemoimmunotherapy as part of induction therapy (e.g., ANBL17P1, ANBL2131 Arm B). Patients with primary refractory disease must have received at least 4 cycles of frontline high-risk induction chemoimmunotherapy * Primary refractory disease following aggressive multi-drug induction chemotherapy on or according to a high-risk NB protocol (e.g., A3973, ANBL0532, ANBL09P1, ANBL12P1, ANBL1531, or ANBL2131 Arm A) with persistent disease at the conclusion of at least 4 cycles of chemoimmunotherapy used as extended induction or pre-consolidation intensification of therapy for primary refractory disease (e.g., ANBL2131 Arm A with extended induction, ANBL1221, or ANBL1821) * NOTE: Patients who experienced disease progression either during or within 30 days of completion (last day of anti-GD2 antibody) of chemoimmunotherapy during induction or extended induction are not eligible for the study * Relapsed/progressive disease * First episode of recurrence following chemoimmunotherapy as part of induction therapy (e.g., ANBL17P1, ANBL2131 Arm B) or extended induction (e.g., ANBL2131 Arm A) * NOTE: Patients who experienced disease progression either during or within 30 days of completion (last day of anti-GD2 antibody) of chemoimmunotherapy during induction or extended induction are not eligible for the study * First episode of recurrent/progressive disease detected during or following chemoimmunotherapy used as part of post-consolidation therapy (e.g., ANBL19P1) * Second episode of recurrent/progressive disease detected during or following chemoimmunotherapy used as first-line salvage therapy for recurrent or progressive disease (e.g., ANBL1221, ANBL1821). Patients with stable disease after receiving chemoimmunotherapy for first relapse are not eligible (must be primary refractory disease) * Evaluable or measurable disease per the revised INRC * Measurable soft tissue disease per Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 that is metaiodobenzylguanidine (MIBG) avid or demonstrates increased FDG uptake on PET scan * Evaluable disease is defined as either: * MIBG-avid lesions only (detected on MIBG scan with positive uptake at minimum of one site that do not meet criteria for measurable disease. This site(s) must represent disease recurrence after completion of therapy, progressive disease on therapy, or refractory disease during induction). OR * New bone site that is avid for FDG-PET (MIBG non-avid tumors) AND has CT/MRI findings consistent with tumor OR has been confirmed by biopsy * Patients with resistant/refractory soft tissue disease that is not MIBG avid or does not demonstrate increased FDG uptake on PET scan must undergo biopsy to document the presence of viable neuroblastoma to be considered a site of disease. Biopsy is not required for patients who have a new site of soft tissue disease or radiographic evidence of disease progression regardless of whether progression occurs while receiving therapy or after completion of therapy * NOTE: Patients with bone marrow only disease are not eligible. Patients with only elevated catecholamines (i.e. \> 2 x ULN) are also not eligible for this study * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients ≤ 16 years of age * For the purposes of this study, "chemoimmunotherapy" is defined as a regimen utilizing any anti-GD2 antibody in combination with cytotoxic chemotherapy, with doses of chemotherapy similar to those used in ANBL1221, ANBL1821, ANBL17P1, ANBL2131, and ANBL19P1 * Patient must have received one and NO MORE THAN one prior chemoimmunotherapy-containing regimen * NOTE: Patients who received ANBL2131 Arm B therapy or a similar regimen including anti-GD2 antibody in combination with chemotherapy and then received an extended induction with chemoimmunotherapy (regardless of whether the chemoimmunotherapy was administered for relapse, progression, or poor end of induction response) will be considered to have received two regimens of chemoimmunotherapy. Similarly, patients who receive chemoimmunotherapy during induction or extended induction and then receive chemoimmunotherapy in post-consolidation (e.g., per ANBL19P1) will be considered to have received two regimens of chemoimmunotherapy. These patients are not eligible for this trial * Patient cannot have received more than two prior lines of therapy, including frontline therapy * Standard high-risk induction with or without extended induction followed by consolidation and post-consolidation immunotherapy with or without eflornithine (DFMO) continuation therapy will be considered one line of therapy * ANBL2131 Arm B induction without extended induction followed by consolidation and post-consolidation immunotherapy with or without DFMO continuation therapy will be considered one line of therapy * NOTE: Induction on ANBL2131 Arm B extended induction, and post-consolidation chemoimmunotherapy are each considered separate regimens for the purposes of counting the number of chemoimmunotherapy regimens. In addition, patients who receive