MV-NIS Infected Mesenchymal Stem Cells in Treating Recurrent Ovarian, Primary Peritoneal or Fallopian Tube Cancer

Inclusion Criteria: * Must have: * Recurrent or progressive ovarian cancer, primary peritoneal cancer or fallopian tube cancer after prior treatment with platinum and taxanes * Histologic confirmation of the original primary tumor * Prior bilateral oophorectomy * The following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's tumor, or adenocarcinoma not otherwise specified (NOS) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, 2 * Absolute neutrophil count (ANC) \>= 1500/uL (obtained =\< 7 days prior to registration) * Platelet (PLT) \>= 100,000/uL (obtained =\< 7 days prior to registration) * Total bilirubin =\< upper normal limit (obtained =\< 7 days prior to registration) * Aspartate aminotransferase (AST) =\< 2 x upper limit of normal (ULN) (obtained =\< 7 days prior to registration) * Creatinine =\< 1.5 x ULN (obtained =\< 7 days prior to registration) * Hemoglobin (Hgb) \>= 9.0 g/dL (obtained =\< 7 days prior to registration) * Normal cardiac function as defined by a normal ejection fraction by MUGA (multi gated acquisition scan) or echocardiogram * Provide informed written consent * Willing to return to Mayo Clinic Rochester for follow-up * Life expectancy \>= 12 weeks * Willing to provide all biologic specimens as required by the pr…