Previous treatment with brentuximab vedotin will be allowed if it was done months prior to enrollment and was not refractory to or had progressive disease (PD) on brentuximab vedotin (BV) Pregnancy or breast-feeding women; breastfeeding should be discontinued if the mother is treated with brentuximab vedotin Brentuximab vedotin naive OR had at least stable disease by Lugano Classification to prior brentuximab vedotin treatment History of prior >= grade hypersensitivity to either brentuximab vedotin or nivolumab Brentuximab vedotin Prior treatment with at least lines of therapy for HL including brentuximab vedotin; in those patients who cannot receive brentuximab vedotin, treatment with prior therapeutic regimens is sufficient Prior treatment with brentuximab vedotin is allowed provided the patient did not progress on BV or within days of last dose of BV; patients must be at least months from the last dose of BV Previous exposure to brentuximab vedotin (BV) Known hypersensitivity to brentuximab vedotin components Histologically confirmed CD-positive (defined in this study as >= % expression) MF (including large cell transformation variant) or SS who have either:\r\n* Received prior systemic therapy (for whom commercial supply of brentuximab vedotin is available) OR\r\n* Not received prior systemic therapy (who will receive brentuximab vedotin free of charge) Previous brentuximab treatment Patient has hypersensitivity to brentuximab vedotin Patients with prior receipt of brentuximab vedotin Patients may have received prior brentuximab vedotin, but must not have received brentuximab vedotin within months prior to registration, and must not have relapsed within months of receiving previous brentuximab vedotin; patients may not have received prior nivolumab or PD/PDL axis agents; patients in the nivolumab/brentuximab cohorts ONLY (D, E, F, Y) may have received prior ipilimumab Patients must not have previously existing hypersensitivity to brentuximab vedotin or ipilimumab RANDOMIZED PHASE II (ARMS K AND L): Patients may have received prior brentuximab vedotin, but must not have received brentuximab vedotin within months prior to registration, and must not have relapsed within months of receiving previous brentuximab vedotin; patients may not have received prior nivolumab or PD/PDL axis agents; patients may not have received prior ipilimumab RANDOMIZED PHASE II (ARMS K AND L): Patients must not have previously existing hypersensitivity to brentuximab vedotin or ipilimumab Resolution of all non-hematologic brentuximab vedotin-related adverse events (AEs) to < grade Intolerance to brentuximab vedotin Patients receiving chronic treatment with systemic steroids; however, patients can receive up to days of steroid therapy prior to starting treatment with brentuximab vedotin (BV)+ doxorubicin, vinblastine, dacarbazine (AVD) May have received either brentuximab vedotin or lenalidomide/immunomodulatory imide drugs (IMiD) without dose modification/delay due to toxicity\r\n* IMiDs defined as thalidomide analogues If received prior brentuximab vedotin or lenalidomide, must be able to tolerate the dose level to which the participant will be enrolled to Allergic reaction/hypersensitivity to lenalidomide or history of anaphylactic shock to brentuximab vedotin in the past Previously untreated with either chemotherapy, radiation therapy or either brentuximab vedotin or nivolumab, or another check point inhibitor Allergy to brentuximab vedotin and/or nivolumab Prior treatment with brentuximab vedotin (BV) Known allergy to bevacizumab or brentuximab vedotin or any of its excipients Previously treated with brentuximab vedotin, immune-oncology agents, or received an allogeneic or autologous stem cell transplant Subjects may be Brentuximab vedotin- nave, or may have had prior Brentuximab vedotin treatment (cohort A, B & C - enrolment closed) Prior treatment with brentuximab vedotin is allowed provided the patient did not progress on BV or within days of last dose of BV; patients must be at least months from the last dose of BV Previous primary progression or grade toxicity on treatment with brentuximab vedotin Participant may have failed to achieve a response or progressed after treatment with brentuximab vedotin or may be brentuximab vedotin nave If female of childbearing age, negative serum pregnancy test within days prior to the first dose of brentuximab vedotin in this study Prior treatment with brentuximab vedotin and bendamustine in combination; may have received prior therapy with brentuximab vedotin or bendamustine separately Received either brentuximab vedotin or bendamustine within months of receiving their first dose of protocol based therapy If brentuximab vedotin or bendamustine was previously received, had disease progression during the first cycles of either brentuximab vedotin or bendamustine Known hypersensitivity to brentuximab vedotin, bendamustine, or mannitol Prior to day of brentuximab vedotin, please verify the patient does not meet the criteria below:\r\n* Symptomatic pulmonary disease currently requiring regular medication including but not restricted to bronchodilators Previous receipt of brentuximab vedotin Please note that there are additional inclusion and exclusion criteria. The study center will determine if you meet all of the criteria. Patients must have received at least prior regimens and have received or be deemed ineligible for autologous stem cell transplant, and must have received prior brentuximab vedotin Previous treatment with brentuximab vedotin Prior use of brentuximab vedotin Must have had prior treatment with brentuximab vedotin or not a candidate for treatment with brentuximab vedotin Prior administration of brentuximab vedotin Previous treatment with brentuximab vedotin or bendamustine. No prior brentuximab vedotin Patient has hypersensitivity to brentuximab vedotin Patient has received other investigational drugs within days before treatment of treatment with brentuximab vedotin Viral, bacterial, or fungal infection within two weeks prior to the first dose of brentuximab vedotin Previous treatment with brentuximab vedotin. Prior use of brentuximab vedotin for GVHD is not allowed; prior use of brentuximab vedotin for the treatment of malignancy is allowed Patient must not have had prior exposure to brentuximab vedotin Prior use of brentuximab vedotin for GVHD is not allowed; prior use of brentuximab vedotin for the treatment of malignancy, i.e. Hodgkin lymphoma, anaplastic large cell lymphoma, etc. is allowed