Dose Dense Paclitaxel With Pembrolizumab (MK-3475) in Platinum Resistant Ovarian Cancer

Inclusion Criteria: * Must have confirmation of the histologic diagnosis of high-grade (grade 2-3) epithelial, non-mucinous, non-borderline, ovarian, fallopian tube, or primary peritoneal carcinoma. May be based on original pathology report or review of original slides. * Willing and able to provide written informed consent/assent and authorization * ≥ 18 years of age on day of signing informed consent * Disease must have been persistent or have recurred within 6 months of prior platinum therapy. Disease may not have progressed during prior platinum therapy (i.e., refractory). * Have measurable disease or detectable (non-measureable) disease * Measurable disease: must have at least one "target lesion" to be used to assess response on this protocol. * Prior Therapy: * Have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound. This initial treatment may have included intraperitoneal therapy, consolidation, non-cytotoxic agents (biologic/ targeted) or extended therapy administered after surgical or non-surgical assessment. If patients were treated initially with paclitaxel for their primary disease, this can have been given weekly or every 3 weeks. The most recent therapy and any therapies subsequent to initial therapy, however, cannot have contained weekly paclitaxel. If the immediate prior (most recent therapy) is the initial therapy, it may not have been with weekly paclitaxel. * Allowed to receive (not required to receive), 2 additional cytotoxic regimens for management of recurrent or persistent disease, with no more than 1 non-platinum regimen. Treatment with weekly paclitaxel for recurrent or persistent disease is NOT allowed. * Allowed to receive(not required to receive), non-cytotoxic (biologic/targeted) therapy as part of their primary treatment regimen. Allowed to receive (not required to receive), non-cytotoxic (biologic/targeted) therapy as part of their treatment for recurrent or persistent disease and/or as treatment for recurrent or persistent disease. If non-cytotoxic (biologic/targeted) therapy is given alone (i.e., not in combination with cytotoxic chemotherapy) it will NOT count as a prior regimen. * Have tissue from an archival tissue sample that has been identified and confirmed as available for study, or newly obtained core or excisional biopsy of a tumor lesion * Have received 1 prior regimen must have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2. If have received 2 or 3 prior regimens, must have an ECOG Performance Status of 0 or 1. * Adequate organ function as defined in the protocol * Recovery from effects of recent surgery, radiotherapy, or chemotherapy: Should be free of active infection requiring antibiotics (with exception of uncomplicated UTI); Any hormonal therapy directed at the malignant tumor must be discontinued at least 2 weeks prior to registration (continuation of hormone replacement therapy is permitted); Any other prior therapy directed at the malignant tumor, including chemotherapy, biologic/targeted and immunologic agents, must be discontinued at least 2 weeks prior to registration and at least 3 weeks before day 1 on trial. * Women of Childbearing Potential (WOCBP): Negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * WOCBP willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Exclusion Criteria: * Have low-grade or non-epithelial cancers, mucinous cancers, and/or borderline low-malignant potential cancers * Currently participating in/have participated in a study of an investigational agent or is or has been using an investigational device within 4 weeks of the first dose of treatment * Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Had a prior monoclonal antibody within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to prior therapies * Had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 3 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. - Note: If received major surgery, must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * History of other invasive malignancies (with exception of non-melanoma skin cancer and or in situ cancers that have undergone potentially curative therapy) are excluded if there is any evidence of other malignancy being present within the last 3 years. Patients are also excluded if their previous cancer treatment contraindicates this protocol therapy. * Have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of ovarian, fallopian tube, or primary peritoneal cancer within the last 3 years are excluded. Prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than 3 years prior to registration, and the patient remains free of recurrent or metastatic disease. * Have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of ovarian, fallopian tube, or primary peritoneal cancer within the last 3 year. May have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than 3 years prior to registration, and the patient remains free of recurrent or metastatic disease. * History of synchronous endometrial cancer unless all of the following conditions are met: Stage not greater than I-A (FIGO 2010 staging criteria); no more than superficial myometrial invasion (\<50%), without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous, clear cell or other FIGO Grade 3 lesions and it has been greater than 3 years since diagnosis and there have been no recurrences. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least 4 weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. * Active autoimmune disease that has required systemic treatment in past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment.. * Evidence of interstitial lung disease, any active, non-infectious pneumonitis, or known active tuberculosis * An active infection requiring systemic therapy * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with participation for the full duration of the trial, or is not in the best interest of the participant, in the opinion of the treating physician or the principal or study investigator. * Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Pregnant or breastfeeding, or expecting to conceive children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody * Known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies) * Known active Hepatitis B or Hepatitis C * Received a live vaccine within 30 days prior to the first dose of trial treatment * Peripheral neuropathy Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or higher * Known hypersensitivity to pembrolizumab or any of its excipients * Known hypersensitivity to paclitaxel * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis.