This randomized phase III trial studies paclitaxel and carboplatin see how well they work compared with paclitaxel and ifosfamide in treating patients with fallopian tube, or peritoneal cavity cancer that is newly diagnosed, persistent, or has come back (recurrent). Drugs used in chemotherapy, such as paclitaxel, carboplatin, and ifosfamide, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether paclitaxel is more effective when given with carboplatin or ifosfamide in treating patients with uterine, ovarian, fallopian tube, or peritoneal cavity cancer.

PRIMARY OBJECTIVES:

I. To determine if treatment with combination paclitaxel and carboplatin (TC) chemotherapy does not result in an inferior death rate when compared to ifosfamide, mesna, and paclitaxel chemotherapy.

SECONDARY OBJECTIVES:

I. To determine if treatment with combination paclitaxel and carboplatin (TC) chemotherapy does not result in an inferior progression-free survival when compared to ifosfamide, mesna, and paclitaxel chemotherapy.

II. To determine if acute toxicity, specifically physician-assessed neurotoxicity and infection, associated with combination paclitaxel and carboplatin chemotherapy is reduced compared to that of ifosfamide, mesna, and paclitaxel chemotherapy.

III. To determine if treatment with combination paclitaxel and carboplatin chemotherapy is associated with superior patient-reported quality of life and neurotoxicity scores compared to that of ifosfamide, mesna, and paclitaxel chemotherapy.

TERTIARY OBJECTIVES:

I. To bank formalin-fixed, paraffin-embedded (FFPE) tumor tissue and deoxyribonucleic acid (DNA) extracted from whole blood for future research.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM I: Patients receive paclitaxel intravenously (IV) over 3 hours followed by carboplatin IV over 30-60 minutes on day 1.

ARM II: Patients receive ifosfamide IV over 1 hour on days 1-3 followed by paclitaxel as in Arm I.

In both arms, treatment repeats every 21 days for 6-10 courses in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up every 3 months for 2 years, every 6 months for 3 years, and then annually thereafter.

Inclusion Criteria:

• Patients must have newly diagnosed stage I-IV, persistent or recurrent (including unstaged) uterine carcinosarcoma (malignant mixed mullerian tumor-MMMT or with ovarian, fallopian tube or peritoneal carcinosarcoma and an enrollment date prior to 10/21/2013; pathology confirmed by site/institutional pathologist prior to enrollment) and be chemotherapy naïve as directed against their carcinosarcoma; unstaged patients (patients who have not had hysterectomy or ovarian surgery) are eligible and should be included as "unstaged" if the only histologic (pathology) documentation of the disease is a biopsy or curettage of the uterus; if these patients have documented metastatic disease, it should be assigned the appropriate stage (III/IV)
• Patients may have received prior adjuvant external beam radiation therapy and/or vaginal brachytherapy; patients should be at least 4 weeks from the completion of external beam radiotherapy prior to beginning protocol chemotherapy; patients do not need to be delayed if receiving vaginal brachytherapy only
• Gynecologic Oncology Group (GOG) performance status 0, 1, or 2
• Patients must have recovered from the effects of recent surgery, radiotherapy, or other therapy
• Patients must be free of active infection requiring antibiotics
• Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to beginning protocol chemotherapy; continuation of hormone replacement therapy is permitted
• Platelet count greater than or equal to 100,000/mcL
• Absolute neutrophil count (ANC) greater than or equal to 1,500/mcL equivalent to Common Terminology Criteria for Adverse Events (CTCAE) version (v)3.0 grade 1
• Creatinine less than or equal to 1.5 times upper limit of normal (ULN), CTCAE v3.0 grade 1
• Bilirubin less than or equal to 1.5 times ULN (CTCAE v3.0 grade 1)
• Serum glutamic oxaloacetic transaminase (SGOT) less than or equal to 2.5 times ULN (CTCAE v3.0 grade 1)
• Alkaline phosphatase less than or equal to 2.5 times ULN (CTCAE v3.0 grade 1)
• Serum albumin should be equal to or greater than 3 g/dL
• Neuropathy (sensory and motor) less than or equal to CTCAE v3.0 grade 1
• Patients must have signed an approved informed consent and authorization permitting release of personal health information
• Patients of childbearing potential must have a negative serum pregnancy test prior to study entry and be practicing an effective form of contraception
• Patients may have measurable disease or non-measurable disease; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be >= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or >= 10 mm when measured by spiral CT; measurable disease patients must have at least one "target lesion" to be used to assess progression on this protocol as defined by Response Evaluation Criteria In Solid Tumors (RECIST); 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

Exclusion Criteria:

• Patients who have received prior cytotoxic chemotherapy for management of uterine or ovarian carcinosarcoma
• Patients with a history of other invasive malignancies or with a concomitant invasive malignancy, with the exception of non-melanoma skin cancer, if there is any evidence of other malignancy being present within the last five years; patients are also ineligible if their previous cancer treatment contraindicates this protocol therapy
• Patients for whom radiotherapy is planned after or during chemotherapy prior to progression of cancer
• Patients with known hypersensitivity to Escherichia (E.) coli-derived drug preparations (pegfilgrastim and filgrastim [G-CSF])
• Patients with a known hypersensitivity to mesna or other thiol compounds
• For enrollment prior to 10/21/2013, patients who are not biopsy proven to have carcinosarcoma of the uterus, fallopian tube, peritoneum or ovary; for enrollment after 10/21/2013, patients who are not biopsy proven to have carcinosarcoma of the uterus