Brentuximab Vedotin + Rituximab as Frontline Therapy for Pts w/ CD30+ and/or EBV+ Lymphomas

Inclusion Criteria: * Histologically confirmed CD30+ and/or EBV+ lymphoid malignancy; in addition, there must be evidence of CD20 expression (at any level) * In cases of post-transplant lymphoproliferative disorder (PTLD) arising in patients who are pharmacologically immunosuppressed, reduction of immunosuppression (RI) must be attempted prior to or in conjunction with enrollment, with the exception of those for whom RI would pose excessive threat of clinically significant graft rejection (as judged by local investigator) * No prior chemotherapy or radiotherapy for PTLD or diffuse large B-cell lymphoma (DLBCL), with the exception of corticosteroids for 10 or fewer days at any dose (no washout period required) * No prior surgical intervention, unless performed for the sake of tissue diagnosis or on an urgent basis for disease-related threat to life, limb, or organ function * Bi-dimensionally measurable disease (at least 1 cm) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count \>= 750/mcL * Platelets \>= 50,000/mcl * Total bilirubin =\< 2 X institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum pyruvate glutamate transaminase \[SPGT\]) =\< 3 X institutional ULN * Creatinine =\< 2 X institutional ULN * NOTE: Patients who do not meet the above criteria because of disease involvement of the organ in question, or because of ac…