Brentuximab Vedotin and Combination Chemotherapy in Treating Patients With CD30-Positive Peripheral T-cell Lymphoma

Inclusion Criteria: * Documented informed consent of participant and/or legally authorized representative * Agreement to allow the use of archival tissue from diagnostic tumor biopsies will be retrieved and submitted post-enrollment * If unavailable, exceptions may be granted with study principal investigator (PI) approval. * Eastern Cooperative Oncology Group (ECOG) status =\< 2 * Histologically confirmed mature peripheral T-cell or natural killer (NK)-cell lymphoma per World Health Organization (WHO) classification, including: * Anaplastic lymphoma kinase (ALK)-positive anaplastic large cell lymphoma (ALCL) with international protein index (IPI) of 2 or higher (must have bulky \[defined as mass \>= 10 cm\] stage II, or stage III-IV disease) * ALK-negative ALCL * NOTE: Per amendment dated 05-10-19, ALCL will no longer be eligible except for Canada. * PTCL-not otherwise specified (NOS) * Angioimmunoblastic T-cell lymphoma (AITL) * Adult T-cell lymphoma/leukemia (ATLL) * Enteropathy-associated T-cell lymphoma (EATL) * Hepatosplenic T-cell lymphoma * CD30-positivity (e.g. at least 1%) by immunohistochemistry confirmed by hematopathology review at the participating institution * Measurable disease of at least 1.5 cm on computed tomography (CT) or positron emission tomography (PET)-CT scan * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * Exception: unless documented bone marrow involvement by lymphoma * Platelets \>= 50,000/mm\^3 * Exception: unle…