Paclitaxel and Carboplatin or Bleomycin Sulfate, Etoposide Phosphate, and Cisplatin in Treating Patients With Advanced or Recurrent Sex Cord-Ovarian Stromal Tumors

Inclusion Criteria: * Patients with histologically confirmed ovarian stromal tumor \[granulosa cell tumor, ganulosa cell-theca cell tumor, Sertoli-Leydig cell tumor (androblastoma), steroid (lipid) cell tumor, gynandroblastoma, unclassified sex cord-stromal tumor, sex cord tumor with annular tubules\] * Patients must have newly diagnosed, stage IIA - IV disease and must be entered within eight weeks from surgery; they may have either measurable residual disease by Response Evaluation Criteria In Solid Tumors (RECIST) criteria, or they may have no measurable residual disease; OR, they must have biopsy-proven recurrent disease of any stage and have never received cytotoxic chemotherapy * Patients must have a Gynecologic Oncology Group (GOG) performance grade of 0, 1, or 2 * Patients of childbearing potential must have a negative serum pregnancy test and must agree to practice an effective means of birth control * Patients in the measureable disease cohort must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST 1.1; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl, equivalent to Common Terminology Criteria for Adverse Events (CTCAE) grade 1 * Platelet greater than or equal to 100,000/mcl * Creatinine no greater than the institutional upper limits of normal * Bilirubin less than or equal to 1.5 x upper limit of normal (ULN) (CTCAE grade 1) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) less than or equal to 3.0 x ULN (CTCAE grade 1) * Alkaline phosphatase less than or equal to 2.5 x ULN (CTCAE grade 1) * Neuropathy (sensory and motor) less than or equal to CTCAE grade 1 * No signs of clinically significant hearing loss * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients must have pulmonary function sufficient to receive bleomycin, with normal lung expansion, absence of crackles on auscultation, and normal carbon monoxide diffusion (DLCO), defined as greater than 80% predicted * Patients with a history of hypersensitivity reactions to prior chemotherapy administered for previous cancer diagnoses are eligible to participate in the study, unless the hypersensitivity reaction consisted of anaphylaxis not amenable to desensitization * Recovery from effects of recent surgery, radiotherapy, or chemotherapy * Patients must be entered within 8 weeks after surgery performed for either 1) initial diagnosis, staging, and/or cytoreduction, or 2) (if done) management of recurrent disease in a chemonaive patient * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration; continuation of hormone replacement therapy is permitted Exclusion Criteria: * Patients who have received any prior cytotoxic chemotherapy or biologics for sex cord-stromal tumors (SCSTs) * Patients with apparent stage I disease who have not undergone a staging procedure * Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer, are excluded if there is any evidence of other malignancy being present within the last five years * Woman who are pregnant or breastfeeding * Patients with medical history or conditions not otherwise previously specified which in the opinion of the investigator should exclude participation in this study; the investigator can consult the study chair or study co-chairs for uncertainty in this regard