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