Inclusion Criteria:

   - Written informed consent

   - Eastern Cooperative Oncology Group (ECOG) performance status of 0-3

   - Life expectancy > 12 weeks

   - Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x upper
   limit of normal (ULN), if caused by ASM/MCL =< 5 x ULN

   - Serum direct bilirubin =< 1.5 x ULN; if considered related to ASM/MCL =< 3 x ULN

   - Serum creatinine =< 2.0 mg/dL

   - A diagnosis of systemic mastocytosis (SM) per 2008 World Health Organization (WHO)
   Criteria

   - Neoplastic mast cells must express CD30 by immunohistochemistry or flow cytometry

   - At least one of the eligible organ damage findings as defined by the international
   consensus response criteria

   - Females of childbearing potential and males who have partners of childbearing
   potential must agree to use an effective contraceptive method during the study and for
   30 days following the last dose of study drug

   - Females of childbearing potential must have a negative serum or urine beta-human
   chorionic gonadotropin (hCG) pregnancy test result within 7 days prior to the first
   dose of SGN-35

   - Females of non-childbearing potential are those who are postmenopausal greater than 1
   year or who have had a bilateral tubal ligation or hysterectomy

Exclusion Criteria:

   - Unwilling or unable to comply with the protocol

   - Any other concurrent severe known disease (except carcinoma in-situ) or concurrent
   severe and/or uncontrolled medical condition (e.g. uncontrolled diabetes, or active
   uncontrolled infection) which could compromise participation in the study

   - History of another primary malignancy that has not been in remission for at least 3
   years (the following are exempt from the 3-year limit: non-melanoma skin cancer, fully
   excised melanoma in situ [stage 0], curatively treated localized prostate cancer, and
   cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on
   Papanicolaou [PAP] smear)

   - Cardiovascular disease including congestive heart failure grade III or IV according to
   the New York Heart Association (NYHA) classification, left ventricular ejection
   fraction of < 50%, myocardial infarction within previous 6 months or poorly controlled
   hypertension

   - Pregnant or lactating

   - Neuropathy greater than or equal to grade 2

   - Known hypersensitivity to any excipient contained in the drug formulation

   - Confirmed diagnosis of human immunodeficiency virus (HIV) infection or active viral
   hepatitis

   - Presenting with an AHNMD requiring immediate cytoreductive therapy or targeted drugs
   (eg, AML)

   - Received any investigational agent, chemotherapy, interferon-alfa, or
   2-chlorodeoxyadenosine (2-CdA, cladribine) within 30 days prior to Day 1

   - Received hematopoietic growth factor support within 14 days of Day 1 of SGN-35

   - Use of prednisone (or equivalent corticosteroid dose) for SM up to 10 mg/day or its
   equivalent is allowed, but it cannot have been started during screening; patients who
   are on prednisone up to 10 mg/day for medical problems unrelated to SM are also
   permitted on study

   - Presence of FIP1L1-PDGFR-alpha fusion even with resistance to imatinib

   - Received any treatment with SGN-35 prior to study entry

   - Any surgical procedure within 14 days of Day 1, excluding central venous catheter
   placement or other minor procedures (eg, skin biopsy)