Platinum Resistant Ovarian Cancer Evaluation of Doxil and Vintafolide (MK-8109, EC145) Combination Therapy (8109-009, EC-FV-04)

Inclusion Criteria: To qualify for randomization and treatment the following criteria must be met: * Subjects must sign an approved informed consent form * Subjects must be ≥ 18 years of age * Subjects must have pathology-confirmed epithelial ovarian, fallopian tube, or primary peritoneal carcinoma * Subjects must have platinum-resistant ovarian cancer, where platinum-resistant is defined as disease that responded to primary platinum therapy and then progressed within 6 months or disease that progressed during or within 6 months of completing secondary platinum therapy * Subjects must have at least a single (RECIST-defined) measurable lesion on a radiological evaluation that is conducted no more than four weeks prior to beginning study therapy (EC145 and/or PLD). * Subjects must have had prior debulking surgery * Subjects must have received prior platinum-based chemotherapy but must not have received more than 2 prior systemic cytotoxic regimens. Subjects are allowed to receive, but are not required to receive, one additional non-cytotoxic regimen for the management of recurrent or persistent disease. Non-cytotoxic (biologic or cytostatic) agents include, but are not limited to, monoclonal antibodies, cytokines, and small-molecule inhibitors of signal transduction. * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Subjects must have recovered (to baseline/stabilization) from prior cytotoxic therapy-associated acute toxicities. Subjects who have recovered from non-cytotoxic therapy-associated toxicity or who have "controlled" non-cytotoxic therapy toxicity (e.g., vascular endothelial growth factor-related hypertension) can be entered into the trial after a drug wash-out period of 4 half lives * Subjects must have adequate organ function including: 1. Bone Marrow Reserve: Absolute neutrophil count(ANC)≥ 1.5x10\^9/L prior to treatment. Subjects on maintenance doses of granulocyte colony stimulating factor (G-CSF) are eligible. Platelets ≥ 100x10\^9/L and hemoglobin ≥ 9 g/dL. 2. Hepatic: Total bilirubin level \< 1.5 x ULN and alanine aminotransferase (ALT), aspartate aminotransferase (AST), gamma glutamyl transferase(GGT), and alkaline phosphatase levels \< 2.5 x ULN. 3. Renal: Serum creatinine level ≤ 1.5 x ULN or creatinine clearance ≥ 50 mL/min/1.73m\^2 for subjects with serum creatinine levels above 1.5 x ULN. 4. Cardiac: Left ventricular ejection fraction (LVEF) equal to or greater than the institutional lower limit of normal. LVEF must be elevated within 90 days prior to Cycle 1 Day 1 * Subjects of childbearing potential must: 1. Have a negative serum pregnancy test prior to initiation of the therapeutic regimen 2. Practice an effective method of birth control (e.g., oral, transdermal or injectable contraceptives, intrauterine device, double-barrier contraception, such as diaphragm and spermicidal jelly) for the duration of their participation in the trial through 3 months following the last dose of study drug. Exclusion Criteria: The presence of any of the following will exclude the subject from the study: * Diagnosis of tumor of low-malignant potential * Prior exposure to PLD or anthracycline therapy * Prior exposure to FR-targeted therapy (EC145, EC0225, farletuzumab, etc) * Prior therapy with mouse antibodies * Prior therapy with vinorelbine (Navelbine®) or vinca-containing compounds * Prior abdominal or pelvic radiation therapy, radiation therapy to \> 10% of the bone marrow, or prior radiation therapy within the past 3 years to the breast/sternum, dermal lesions, head or neck * Recent (i.e., ≤ 6 weeks) history of abdominal surgery or peritonitis * Serious comorbidities (as determined by the investigator) such as, but not limited to, active congestive heart failure or recent myocardial infarction. Subjects who require antifolate therapy for the management of comorbid conditions (e.g., rheumatoid arthritis) will be excluded from the trial. * Pregnancy * Concurrent malignancy or history of other cancer (except noninvasive skin cancer) within the last 5 years * Symptomatic central nervous system metastasis * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy that is considered to be investigational (i.e., used for non-approved indications(s) and in the context of a research investigation). Use of low dose corticosteroid therapy (for nausea prophylaxis, etc) is acceptable; however, concomitant tamoxifen therapy is not. Supportive care measures are allowed.