Inclusion Criteria:

- Histologically or cytologically confirmed ovarian epithelial, fallopian tube, or
primary peritoneal cancer, including one of the following epithelial cell types*:

- Serous adenocarcinoma

- Endometrioid adenocarcinoma

- Mucinous adenocarcinoma

- Undifferentiated carcinoma

- Clear cell adenocarcinoma

- Mixed epithelial carcinoma

- Transitional cell carcinoma

- Malignant Brenner tumor

- Adenocarcinoma not otherwise specified

- Persistent or recurrent disease (either "platinum-sensitive" or platinum-resistant")

- Has failed primary therapy AND 1-2 second-line therapies

- No more than 3 prior second-line therapies in the recurrent disease setting

- Measurable or detectable disease

- Measurable disease defined as ≥ 1 lesion that can be accurately measured in ≥ 1
dimension with the following:

- Lesion must be ≥ 10 mm by CT scan, MRI, or caliper measurement by clinical
exam, OR ≥ 20 mm by chest x-ray

- Lymph nodes must be ≥ 15 mm in short axis by CT scan or MRI

- Detectable disease defined as any of the following:

- CA-125 baseline values of ≥ 2 times upper limit of normal

- Ascites and/or pleural effusion attributed to tumor

- Solid and/or cystic abnormalities on radiographic imaging that do not meet
RECIST 1.1 definitions for target lesions

- No synchronous primary endometrial cancer or history of primary endometrial cancer
unless the primary origin of the recurrent or persistent tumor is ovarian or
peritoneal AND all of the following criteria are met:

- Stage of endometrial cancer is ≤ IB

- No more than superficial myometrial invasion without vascular or lymphatic
invasion

- No poorly differentiated subtypes, including papillary serous, clear cell, or
other FIGO grade 3 lesions

- No known brain metastases

- GOG performance status 0-2

- ANC ≥ 1,500/mm^3 (not induced or supported by granulocyte colony-stimulating factors)

- Platelet count ≥ 100,000/mm^3

- Creatinine normal

- Calculated creatinine clearance > 50 mL/min

- Bilirubin ≤ 1.5 times upper limit of normal (ULN)

- SGOT ≤ 3 times ULN

- Alkaline phosphatase ≤ 2.5 times ULN

- INR ≤ 1.5 times ULN (or 2-3 for patients on a stable dose of therapeutic warfarin)

- PTT ≤ 1.5 times ULN

- Heparin, low molecular weight heparin, or alternative anticoagulants allowed

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No other invasive malignancies within the past 5 years except nonmelanoma skin cancer
and localized breast cancer, including localized cancer of the breast, head and neck,
or skin adequately treated for > 3 years with no evidence of disease recurrence

- Neuropathy (sensory and motor) < grade 1

- No myocardial infarction within the past 12 months

- No new evidence of acute ischemia or conduction abnormalities by ECG

- No concurrent uncontrolled illness including, but not limited to, any of the
following:

- Ongoing or active infection requiring parenteral antibiotics

- Acute hepatitis

- Symptomatic congestive heart failure

- Unstable angina pectoris

- Cardiac arrhythmia

- Psychiatric illness or social situation that would limit compliance with study
requirements

- No active infection requiring antibiotics except for uncomplicated urinary tract
infection

- No history of allergic reactions attributed to carboplatin or compounds of similar
chemical or biologic composition to bortezomib, including boron or mannitol

- No insulin-dependent diabetes

- No other concurrent investigational agents

- Must have had 1 prior platinum-based chemotherapeutic regimen for management of
primary disease containing carboplatin, cisplatin, or another organoplatinum compound
that included any of the following:

- Non-cytotoxic therapy

- Intraperitoneal therapy

- Consolidation therapy

- Extended therapy

- At least 1 prior cytotoxic regimen for the management of recurrent of persistent
disease

- Recovered from the effects of recent surgery, radiotherapy, or chemotherapy

- No prior bortezomib

- No prior cancer treatment that would contraindicate study treatment

- At least 1 week since prior hormonal therapy directed at the malignant tumor

- Continuation of hormone replacement therapy allowed

- At least 3 weeks since any other therapy directed at the malignant tumor, including
biological and immunologic agents

- No prior radiotherapy or chemotherapy for any abdominal or pelvic tumor other than
ovarian cancer

- More than 3 years since prior radiotherapy for localized cancer of the breast,
head and neck, or skin that remains free of recurrence or metastatic disease
allowed

- More than 3 years since prior adjuvant chemotherapy for localized breast cancer
that remains free of recurrence or metastatic disease allowed

- Concurrent ovarian estrogen and/or progestin replacement therapy for control of
menopausal symptoms allowed provided it is administered at the lowest effective
dose(s)

- No concurrent progestins for the management of anorexia

- No concurrent prophylactic growth factors (filgrastim, sargramostim, or pegfilgrastim

- No concurrent amifostine or other protective reagents