Positive serologic or polymerase chain reaction (PCR) test results for acute or chronic hepatitis B virus (HBV) infection Microsatellite stable disease determined by IHC and/or polymerase chain reaction (PCR). Serologic status and/or polymerase chain reaction (PCR) testing reflecting active hepatitis B or C infection Documented human immunodeficiency virus (HIV) infection or positive serology, active bacterial infections, serologic or polymerase chain reaction (PCR) evidence for active or chronic hepatitis B or hepatitis C Active Hepatitis B (by surface antigen expression or polymerase chain reaction) or C (by polymerase chain reaction) infection or on hepatitis-related antiviral therapy within 6 months of first dose of study drug. EGFRvIII, the target antigen, must be identified on tumor tissue by immunohistochemistry (IHC) or polymerase chain reaction (PCR), i.e. EGFRvIII positive via pathology report Positive test for hepatitis C antibody (patients with documented clearance of hepatitis C by polymerase chain reaction [PCR] following treatment will be permitted) Active hepatitis B infection as documented by positive hepatitis B polymerase chain reaction (PCR) assay Human immunodeficiency virus (HIV)-positive patients regardless of treatment are excluded; patients with evidence of active hepatitis B and hepatitis C infection with positive real time polymerase chain reaction (qPCR) are also excluded but patients with prior exposure to hepatitis B or C with negative qPCR are allowed Active hepatitis C, defined by the detection of hepatitis C ribonucleic acid (RNA) in plasma by polymerase chain reaction (PCR) Positive study for Hepatitis B surface antigen or Hepatitis B or C confirmed by polymerase chain reaction (PCR) Known to be positive for hepatitis B by surface antigen expression; known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) Documentation of HPV tested by polymerase chain reaction (PCR) Active hepatitis C, defined by the detectable hepatitis C ribonucleic acid (RNA) in plasma by polymerase chain reaction (PCR) Expression of one (1) or more of the following TAPAs: SP17, AKAP4, Ropporin, PTTG1 and Span-xb, by either reverse transcriptase polymerase chain reaction (RT-PCR) and/or immunocytochemistry, Western blotting or ELISA, in neoplastic cells and/or blood. The presence of the target antigen, EGFRvIII, must be identified on tumor tissue by immunohistochemistry (IHC) or polymerase chain reaction (PCR) Presence of human immunodeficiency virus (HIV) (antibody [Ab] positivity), or active hepatitis A, B or C infection (active infection will be defined as hepatitis A immunoglobulin M [IgM] Ab positivity, hepatitis B surface Ag positivity, or hepatitis C polymerase chain reaction [PCR] positivity, respectively) Detectable circulating tumor cells (CTCs) with detectable AR?V7 splice?variant by reverse transcriptase (RT)?polymerase chain reaction (PCR) Patients known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months), or with known human immunodeficiency virus (HIV) infection Patients known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months); patients with history of human immunodeficiency virus (HIV) disease are also excluded from the study Known to be positive for hepatitis B by surface antigen expression; known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) Active hepatitis B or hepatitis C (virus detectable by polymerase chain reaction [PCR]) Rapid influenza diagnostic test (RIDT), polymerase chain reaction (PCR), or viral culture positive for influenza A diagnosis of APL based on the presence of the PML-RAR-alpha fusion gene by cytogenetics, polymerase chain reaction (PCR), or POD test Untreated HIV or active hepatitis C detectable by polymerase chain reaction (PCR), or chronic hepatitis B (patients positive for hepatitis B core antibody who are receiving intravenous immunoglobulin (IVIG) are eligible if hepatitis B [HepB] polymerase chain reaction [PCR] is negative). Known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg] reactive) or known active hepatitis C virus (by polymerase chain reaction [PCR]) Diagnosis of advanced stage or metastatic HER2-positive cancer (immunohistochemistry or reverse transcriptase-polymerase chain reaction [RT-PCR] is used to determine HER2 positivity) Active Hepatitis B (by surface antigen expression or polymerase chain reaction) or C (by polymerase chain reaction) infection or on hepatitis-related antiviral therapy within 6 months of first dose of study drug. Known to have active hepatitis C infection (positive by polymerase chain reaction) or on antiviral therapy for hepatitis C within 6 months prior to the first doses of brentuximab vedotin and lenalidomide Patients known to be positive for hepatitis B by surface antigen expression; known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) MART-1 positive melanoma by reverse transcription (RT)-polymerase chain reaction (PCR) or immunohistochemistry (IHC) Patients known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) or with a history of human immunodeficiency virus (HIV) disease Participants must demonstrate evidence of persistent disease either by cytogenetics/FISH or by polymerase chain reaction (PCR) for BCR/ABL in the peripheral blood or bone marrow Active hepatitis b virus (positive hepatitis b surface antigen) or active hepatitis c virus (measurable viral ribonucleic acid [RNA] load with polymerase chain reaction) infection Active hepatitis B infection as documented by positive hepatitis B polymerase chain reaction (PCR) assay Known to be positive for hepatitis B by surface antigen expression; known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months); known to be active cytomegalovirus (CMV) infection or herpes zoster infection Known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) Must have HERV-K(HML2) viral load of >= 1 x 10^4 using a gag primer reverse transcriptase (RT)-polymerase chain reaction (PCR) assay Subjects meeting the following criteria will be excluded from enrollment in the pre-phase arm of the study, but may be included in the GA only arm\r\n* Contraindication to use rituximab or prednisone including:\r\n** Uncontrolled diabetes mellitus\r\n** Systemic fungal infection\r\n** Evidence of active hepatitis B infection (i.e. patients testing positive for hepatitis B surface antigen or viral deoxyribonucleic acid [DNA] by polymerase chain reaction [PCR] analysis) will be excluded; patients with evidence of past infection without active viremia (i.e. positive hepatitis B DNA PCR) will be treated with entecavir as per institutional guidelines and may be included in the study\r\n** History of any serious adverse reaction to either a corticosteroid or rituximab not including rituximab infusion reactions =< grade 3 Patients with active Hepatitis B or C viral replication by polymerase chain reaction (PCR) Patients with active hepatitis B or C determined by polymerase chain reaction (PCR) Serologic status and/or polymerase chain reaction (PCR) testing reflecting active hepatitis B or C infection