SJG-136 in Treating Patients With Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancer That Did Not Respond to Previous Treatment With Cisplatin or Carboplatin

Inclusion Criteria: * Must have persistent or recurrent epithelial ovarian, primary peritoneal, or fallopian tube carcinoma, with histologic confirmation of the original primary tumor. * Must have had at least one prior platinum-based (cisplatin or carboplatin) chemotherapy regimen for the management of their primary disease. This would include intraperitoneal chemotherapy. * Must be considered platinum refractory or resistant, defined as patients with progression of disease during platinum-based chemotherapy, patients having persistent disease at the completion of platinum-based chemotherapy, or patients having a disease free interval following prior platinum therapy of less than six months. * May have had no more than three prior treatment regimens for their epithelial ovarian, primary peritoneal or fallopian tube carcinoma. Consolidation or maintenance therapy initiated within six weeks of the completion of primary therapy will not be counted as an additional regimen. * Must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2. * Time interval from last chemotherapy, radiotherapy, or surgery of at least four weeks and the patient must have recovered from any significant adverse effects of prior treatment. Patients must be at least six weeks from having received nitrosoureas or mitomycin C. * Life expectancy greater than three months. * Must have adequate bone marrow and organ function: * Leukocyte count \> 3 x 10\^9/L * Absolute neutrophil count (ANC) \> 1.5 x 10\^9/L * Platelet count \> 100 x 10\^9/L * Total bilirubin Within normal institutional limits * Aspartate aminotransferase (AST)/alanine transaminase (ALT) \< 2.5 x institutional upper limits of normal * Creatinine \< 1.5 mg/dL or calculated creatinine clearance (ClCr) \> 60 ml/min by Cockcroft Gault method, as below. ClCr = weight (kg) x (140-age) x 0.85 72 x serum creatinine (mg/dL) * Participants must have signed an approved informed consent. * Participants of childbearing potential must have a negative serum pregnancy test prior to study entry and must use an effective form of contraception. * Must have archival tissue available from their original tumor debulking surgery for assessment of BRCA1 protein expression. Exclusion Criteria: * Patients with borderline ovarian tumors, ovarian germ cell tumors, ovarian sex-cord stromal tumors, or other non-epithelial ovarian tumors are not eligible. * Patients receiving any other investigational agents. * Patients who have received radiation therapy to more than 25% of the bone marrow. * Patients who have previously received SJG-136 or related compounds. * Uncontrolled intercurrent illness including, but not limited to, ongoing active infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmias, or psychiatric illness/social situations that would limit compliance with the study requirements. * Prior malignancy (other than cervical carcinoma in situ, ductal carcinoma in situ of the breast, or non-melanoma skin cancer) unless treated with curative intent and without evidence of disease for three years. * With the exception of alopecia (or other situations in which the organ dysfunction or symptoms are considered clinically insignificant or irrelevant to the study), patients may not have baseline organ dysfunction or symptoms that qualify as grade 2 or higher by the CTEP Common Toxicity Criteria for Adverse Effects (CTCAE) v4.0. Particular attention should be paid to assessment of pre-existing edema, since vascular leak syndrome was the dose limiting toxicity of this agent in the phase I trial.