Brentuximab Vedotin Before Autologous Stem Cell Transplant in Treating Patients With Hodgkin Lymphoma

Inclusion Criteria: * Patients must have histologically documented or cytologically confirmed Hodgkin lymphoma with CD 30 expression * Patients must have absolute neutrophil count (ANC) \>= 1000/uL; neupogen (filgrastim) can be given prior to start of SGN-35 (brentuximab vedotin) and during SGN-35 treatment to achieve target ANC \>= 1000/uL * Patients must have platelets (Plts) \>= 50,000/uL; platelet transfusion can be given prior to the start of SGN-35 and during SGN-35 treatment to achieve a target plt \>= 50,000/uL * Patients must have measurable disease \> 1.5 cm evidenced by computed tomography (CT) scan of the neck/chest/abdomen(abd)/pelvis or CT/positron emission tomography (PET) scans * Patient must be either primary refractory to one frontline induction therapy or relapsed after one frontline induction therapy; patients who do not achieve complete remission after induction therapy are also eligible * Patients cannot have had a second line salvage treatment (chemotherapy, biologic agents, investigational drugs, or radiation) or have had an autologous or allogeneic hematopoietic stem cell transplantation; patients can have had mixed frontline therapy such as 2-4 cycles of ABVD (doxorubicin, bleomycin, vinblastine and dacarbazine) followed by 2-4 cycles of bleomycin, etoposide, doxorubicin, cyclophosphamide, vincristine, procarbazine, and prednisone (BEACOPP) as long as the induction chemotherapy is not more than 8 cycles in total length * Radiation use as part of induction regimen or consolidation (within 90 days after completion of induction chemotherapy) is allowed * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study * Male subject agrees to use an acceptable method of contraception for the duration of the study * Life expectancy of greater than 3 months * Karnofsky performance status of \> 60% * ANC \>= 1000/uL * Plts \>= 50,000/uL * Total bilirubin within 1.5 x of the upper limit of normal (ULN) institutional limits, patients with elevation of unconjugated bilirubin alone, as in Gilbert's disease, are eligible * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) \< 2.5 X institutional ULN (unless demonstrated Hodgkin lymphoma involvement of the liver) * Calculated creatinine clearance \>30 ml/min (unless demonstrated Hodgkin lymphoma involvement of the kidney) ELIGIBILITY FOR 2.4 MG/KG DOSING IN THE NEW COHORT: \- In addition to the inclusion/exclusion criteria outlined, to be eligible for treatment with the higher 2.4 mg/kg dose of brentuximab vedotin in the new cohort of 20 additional patients, best response after 2 cycles of brentuximab vedotin administered at the 1.8 mg/kg dose, must be partial remission (PR) or stable disease (SD) as determined by radiographic imaging Exclusion Criteria: * Patient has \> 1.5 x ULN total bilirubin, unless history of Gilbert's syndrome * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant * Patient has hypersensitivity to brentuximab vedotin * Female subject is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * Patient has received other investigational drugs within 14 days before treatment of treatment with brentuximab vedotin * Serious medical or psychiatric illness likely to interfere with participation in this clinical study * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy * Patients with other active malignancies (no evidence of other cancer or life expectancy greater than 5 years) are ineligible for this study * Patients with active central nervous system (CNS) disease or history of brain metastases (mets) are excluded from study * Patients may be on steroids prior to initiation of treatment as long as by cycle 1 day 1 steroids use was tapered down less than or equal to 20 mg of prednisone.