Brentuximab Vedotin With or Without Nivolumab in Treating Patients With Relapsed or Refractory CD30+ Lymphoma

Inclusion Criteria:

* Relapsed or refractory CD30+ lymphoma that has either achieved \< PR to brentuximab vedotin (minimum of 2 cycles), progressed while receiving brentuximab vedotin, or progressed within 6 months of the last dose of brentuximab vedotin
* Documented expression of CD30 on tumor cells
* Absolute neutrophil count (ANC) \> 1,000/uL
* Platelets \> 50,000/uL
* Serum creatinine \< 1.5 mg/dL OR creatinine clearance \> 60 mL/min
* Bilirubin \< 1.5 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 x ULN
* Measurable disease by computed tomography (CT) or similar (e.g. magnetic resonance imaging \[MRI\]) criteria (\> 1.5 cm). (Patients with cutaneous lymphoma only require measurable disease by Olsen Criteria)
* Age \>= 18 yrs at the time of the first dose of study drug
* Resolution of all non-hematologic brentuximab vedotin-related and nivolumab-related adverse events (AEs) to \< Grade 2
* All patients must be informed of the investigational nature of this study and have given written consent in accordance with institutional and federal guidelines
* Patients must be anticipated to complete at least 2 cycles of chemotherapy on study
* Expected survival if untreated of \> 90 days

Exclusion Criteria:

* Prior transplant within 100 days
* Radioimmunotherapy within 12 weeks
* Known human immunodeficiency virus (HIV) or hepatitis B positivity or prior progressive multifocal leukoencephalopathy (PML)
* Active infection or other medical condition which would preclude treatment in the opinion of the principal investigator; this would include a corrected diffusing capacity of the lungs for carbon monoxide (DLCO) of \< 60% predicted or symptomatic interstitial lung disease
* Eastern Cooperative Oncology Group (ECOG) performance status \> 2
* Known active central nervous system (CNS) involvement
* Peripheral neuropathy \> grade 1 if due to brentuximab vedotin or any peripheral neuropathy \> grade 2
* Intolerance to brentuximab vedotin
* Concurrent use of other anti-cancer agents or experimental treatments
* No current or prior autoimmune disease with the exception of vitiligo and autoimmune alopecia (Arm B only)
* Pregnancy or breastfeeding; (females of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin \[beta-hCG\] pregnancy test result within 7 days prior to the first dose of brentuximab vedotin; females with false positive results and documented verification that the patient is not pregnant are eligible for participation; females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy; females of childbearing potential and males who have partners of childbearing potential must agree to use 2 effective contraceptive methods during the study and for 6 months following the last dose of brentuximab vedotin or 6 months following the last dose of nivolumab, whichever is later)