Inclusion Criteria:  Patients must have histologically determined classic Hodgkin lymphoma with pathologic review at the participating institution. Participants must have measurable disease, defined as a lymph node or tumor mass ≥1.5 cm in at least one dimension by CT, PET/CT, or MR. Imaging must have been completed no greater than 6 weeks prior to study enrollment. Measurable disease that has previously been irradiated is permissible only if there has been evidence of progression since the radiation. Patients must have progressed after two or more lines of systemic treatment, including autologous stem cell transplantation, if eligible.  Patients must have received a prior PD-1 monoclonal antibody, with the following specific requirements for each cohort.  Cohort 1  Received 18-30 weeks of single-agent PD-1 mAb (with last dose within 12 weeks)  Underwent a restaging PET scan 18-30 weeks after initiation of PD-1 monotherapy which demonstrated:  Partial response or stable disease (based on Lugano criteria) Note: Patients achieving an indeterminate response based on LYRIC criteria(23) on an initial staging PET scan are eligible if they achieve stable disease (<10% increase in tumor burden and <50% decrease in tumor burden) or a partial response on a subsequent staging PET scan.  Cohort 2  Progression of disease or relapse following treatment with nivolumab or pembrolizumab. Intervening treatments between PD-1 mAb therapy and the trial are permitted. Patients may have had a prior autologous stem cell transplant and may have been treated with chimeric antigen receptor T-cells (CAR T-cells). Age ≥18 years. Eastern Cooperative Oncology Group (ECOG) performance status 0-2 (see Appendix A)  Adequate hematologic and organ function as defined below:  Absolute neutrophil count > 1.0x109/L unless due to marrow involvement by lymphoma in which case ANC must be >0.75x109/L. Growth factor support is allowed provided it is received at least 5 days prior to enrollment labs. Platelets > 75 x109/L, unless due to marrow involvement by lymphoma, in which case platelets must be >50 x109/L Estimated GFR (by Cockroft-Gault equation) > 40ml/min Total bilirubin < 1.5 X ULN AST/ALT < 2.5 X ULN Ability to understand and the willingness to sign a written informed consent document. Willingness to provide pre-treatment tumor sample by core needle or excisional surgical biopsy. An archival sample is acceptable in the following situations: the sample was acquired within 90 days of initiation of PD-1 therapy AND the following provisions are met: 1) availability of a tumor-containing formalin fixed, paraffin embedded (FFPE) tissue block, 2) if the tumor containing FFPE tissue block cannot be provided in total, sections from this block should be provided that are freshly cut and mounted on positively charged glass slides (SuperFrost Plus are recommended). Preferably, 25 slides should be provided; if not possible, a minimum of 15 slides is required. Exceptions to this criterion may be made with approval of the Study Chair. Willingness to use contraception during and after study treatment. Women of child-baring potential (WOCBP) will be instructed to adhere to contraception for a period of 5 months following last dose of nivolumab and 6 months following the last dose of ipilimumab. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 7 months after last dose of nivolumab and 6 months after the last dose of ipilimumab.  Exclusion Criteria:  Patients currently receiving anticancer therapies or who have received anticancer therapies within 28 days of the start of study drug (including chemotherapy, radiation therapy, antibody-based therapy, etc.), or 56 days for radioimmunotherapy. Steroids for symptom palliation are allowed but must be either discontinued or on stable doses of < 10mg daily of prednisone (or the equivalent) at the time of initiation of protocol therapy. Patients may not be receiving any other investigational agents or have received investigational agents within 4 weeks (or 3 half-lives, whichever is longer) of beginning treatment. History of severe allergic or anaphylactic reactions to monoclonal antibody therapy unless in consultation with an allergy specialist they are deemed eligible for retreatment with desensitization. Patients who have undergone prior allogeneic stem cell transplantation Patients with a history of or active autoimmune disease (except controlled asthma, Hashimoto thyroiditis, atopic dermatitis, or vitiligo), or requiring systemic corticosteroids at a dose of 10mg prednisone equivalent daily. Patients with a history of autoimmune disease who never required corticosteroids and with no evidence of disease activity, and in whom the risk of reactivation is felt not to be serious, may be enrolled after discussion with the overall study chair. Exceptions to this are patients with a history of inflammatory bowel disease (ulcerative colitis and Crohn's disease). These patients are excluded regardless of whether their disease is active or inactive. Patients who experienced grade 4 immune-related adverse events (irAEs) during treatment with a PD-1 mAb. Patients with active pneumonitis or colitis, or patients with cirrhosis. Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia). Patients with known HIV infection or hepatitis B or C infection. Testing for HIV is optional. Testing for hepatitis B and C is mandatory. Patients with hepatitis B core Ab positivity but negative surface antigen and negative viral load may be enrolled if they can be treated with a prophylactic agent (eg, entecavir); patients with hepatitis C seropositivity who have a negative viral load can also be enrolled. Patients with a systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment). Prior history of another malignancy (except for non-melanoma skin cancer or in situ cervical or breast cancer) unless disease free for at least 2 years. Patients with prostate cancer are allowed if PSA is less than 1. Patients should not have received immunization with attenuated live vaccine within one week of study entry or during study period. History of noncompliance to medical regimens. Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study. Patients with any one of the following currently on or in the previous 6 months will be excluded: myocardial infarction, congenital long QT syndrome, torsade de pointes, left anterior hemiblock, unstable angina, coronary/peripheral artery bypass graft, or cerebrovascular accident. Other uncontrolled intercurrent illness that would limit adherence to study requirements.