This phase I/II trial studies the side effects and best dose of brentuximab vedotin that can be combined with ifosfamide, carboplatin, and etoposide in treating patients with Hodgkin lymphoma that has come back (relapsed) or is not responding to treatment (refractory). Monoclonal antibody-drug conjugates, such as brentuximab vedotin, can block cancer growth in different ways by targeting certain cells. Chemotherapy drugs, such as ifosfamide, carboplatin, and etoposide, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving brentuximab vedotin together with an ifosfamide, carboplatin, and etoposide chemotherapy regimen may kill more cancer cells.

PRIMARY OBJECTIVES:

I. To determine maximally tolerated dose of brentuximab vedotin that can be combined with ifosfamide, carboplatin and etoposide chemotherapy in patients with relapsed or refractory Hodgkin lymphoma.

II. To gain a preliminary assessment of the efficacy of the above regimen.

SECONDARY OBJECTIVES:

I. To determine the safety and toxicity of the above regimen.

II. To determine the ability to proceed to peripheral blood stem cell collection following the above regimen (the impact of above regimen on stem cell reserve).

III. To assess the impact of this regimen on biomarkers from the microenvironment in Hodgkin lymphoma tumors.

OUTLINE: This is a phase I, dose-escalation study of brentuximab vedotin followed by a phase II study.

Patients receive brentuximab vedotin intravenously (IV) over 30 minutes on days 1 and 8; ifosfamide IV over 24 hours and carboplatin IV over 1 hour on day 2; and etoposide IV over 1 hour on days 1-3. Treatment repeats every 21 days for 2 courses in the absence of disease progression or unacceptable toxicity. Patients planning to go on to consolidative high-dose therapy (HDT) and autologous stem cell transplantation (ASCT) may undergo peripheral blood stem cell (PBSC) mobilization following the 2nd course of study therapy at the discretion of the treating physician.

After completion of study treatment, patients are followed up every 3 months for 1 year and then every 6 months for 4 years.

Inclusion Criteria:

• Patients must have primary refractory or first relapse of cluster of differentiation 30 (CD30)+ Hodgkin lymphoma
• Patients must have measurable disease defined as lesions that can be accurately measured in two dimensions by computed tomography (CT), magnetic resonance imaging (MRI), medical photograph (skin or oral lesion), plain x-ray, or other conventional technique and a greatest transverse diameter of 1 cm or greater; or palpable lesions with both diameters >= 2 cm; further, at least 1 of these lesions must be positive by positron emission tomography (PET) scan (i.e., Deauville score of 4 or more); Note: CT scans remain the standard for evaluation of nodal disease
• Patients must have a CT of chest, abdomen, and pelvis with PET within 28 days of enrollment; patients with evidence of lymphadenopathy in the neck must have a dedicated CT of neck
• Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (performance status of 2 will be allowed if poor performance status is thought to be directly secondary to patient's Hodgkin lymphoma [HL])
• Absolute neutrophil count (ANC) >= 1,500/uL, performed within 28 days prior to registration
• Platelets >= 100,000/uL (without transfusion or growth factor support), performed within 28 days prior to registration
• Serum creatinine < 1.5 mg/dl or creatinine clearance (CrCl) > 60 mL/min, performed within 28 days prior to registration
• Total bilirubin < 2 times upper limit of normal (unless due to Gilbert's syndrome), performed within 28 days prior to registration
• Aspartate aminotransferase (AST) < 2.5 times upper limit of normal, performed within 28 days prior to registration
• All patients must be informed of the investigational nature of this study and have given written consent in accordance with institutional and federal guidelines
• Patients must be anticipated to complete 2 cycles of chemotherapy

Exclusion Criteria:

• Patients known to be positive for human immunodeficiency virus (HIV)
• Pregnant or nursing women; men or women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method
• Patients with other prior malignancies except for adequately treated basal cell carcinoma, squamous cell carcinoma of the skin, breast or cervical cancer in situ, or other cancer from which the patient has been disease-free for 5 years or greater, unless approved by the protocol chair or co-chair
• Patients with known allergy, intolerance, or resistance (i.e., remission duration less than 6 months or lack of response) to ifosfamide, carboplatin, or etoposide
• Patients with evidence of active central nervous system lymphoma
• Patients with prior receipt of brentuximab vedotin
• Patients with peripheral neuropathy of > grade 1
• Patients who have other medical conditions that would contraindicate treatment with aggressive chemotherapy (including active infection, uncontrolled hypertension, congestive heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, or uncontrolled arrhythmia); if the patient's cardiac history is questionable, a measurement of left ventricular ejection fraction should be obtained within 42 days prior to registration; patients with left ventricular ejection fraction < 50% are not eligible
• Prior failed (< 5 x 10^6 CD34/kg) peripheral blood stem cell (PBSC) collection
• Patients who had pelvic radiation within 12 months
• Previous chemotherapy/immunotherapy within 3 weeks before study entry
• Concurrent use of other anti-cancer agents or experimental treatments