Brentuximab vedotin has previously been combined in another study with a different standard of care chemotherapy regimen: cyclophosphamide, doxorubicin, and prednisone. The study included patients with various types of T-cell lymphomas. Two of the patients enrolled in that study had ATLL. Both had a complete response (no evidence of disease). The researchers in the current study (LCCC 1637) have added etoposide to the combination of brentuximab vedotin with cyclophosphamide, doxorubicin, and prednisone. They predict that the addition of etoposide will improve patient outcomes. Research shows that etoposide helps improve outcomes in patients with certain types of T-cell lymphomas who undergo chemotherapy treatment. This investigational combination of brentuximab vedotin with cyclophosphamide, doxorubicin, etoposide, and prednisone is called BV-CHEP.