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: unless documented bone marrow involvement by lymphoma * Total serum bilirubin =\< 1.5 x upper limit of normal (ULN) OR if hepatic involvement by lymphoma: =\< 3 x ULN for Gilbert's disease or documented hepatic involvement by lymphoma * Aspartate aminotransferase (AST) =\< 2 x ULN OR if hepatic involvement by lymphoma: AST =\< 5 x ULN * Alanine aminotransferase (ALT) =\< 2 x ULN OR if hepatic involvement by lymphoma: ALT =\< 5 x ULN * Creatinine clearance of \>= 60 mL/min per the Cockcroft-Gault formula * Left ventricular ejection fraction (LVEF) \>= 45% * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by WOCBP and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy; childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Prior treatment of PTCL with systemic anti-lymphoma therapies, investigational agents, radiation * Exception: May have received 1 cycle of CHOP-like therapy (e.g. CHOP, CHOEP, EPOCH) or 1 cycle of CHP-BV; these participants must initiate day 1 cycle 1 of study therapy (CHEP-BV) no less than 19 days from prior CHOP-like or CHP-BV therapy; Patients who received 1 cycle of CHOP-like or 1 cycle of CHP-BV therapy prior to initiating induction with CHEP-BV are allowed to receive only 5 cycles of CHEP-BV instead of 6 cycles, per investigator's discretion * History of another primary invasive cancer, hematologic malignancy, or myelodysplastic syndrome that has not been in remission for at least 3 years. * Exceptions: Non-melanoma skin cancer and in situ cervical cancer * Symptomatic cardiac disease (including symptomatic ventricular dysfunction, symptomatic coronary artery disease, and symptomatic arrhythmias), cerebrovascular event/stroke or myocardial infarction within the past 6 months * Central nervous system involvement by lymphoma, including leptomeningeal involvement * History of progressive multifocal leukoencephalopathy (PML) * Active \>= grade 3 viral, bacterial, or fungal infection within 2 weeks prior to day 1 of protocol therapy * Any known human immunodeficiency virus (HIV) infection, hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection * Baseline peripheral neuropathy \>= grade 2 or patients with the demyelinating form of Charcot-Marie-Tooth syndrome * Known severe hypersensitivity to any study related agent excipient(s) * Females only: pregnant or breastfeeding * Any other condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)