Carboplatin/Taxol/Ridaforolimus in Endometrial, Ovarian and Solids

Inclusion Criteria: * Must have measurable disease or evaluable 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 a minimum size of 10 mm by CT scan (CT scan slice thickness no greater than 5 mm), 10 mm caliper measurement by clinical exam or 20 mm by chest X-ray. Lymph node must be ≥ 15 mm in short axis when assessed by CT scan. Evaluable disease is disease evident on imaging that does not meet Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1, however, meets tumor marker evaluation, e.g., Gynecologic Cancer Intergroup (GCIG) criteria. Notes: i) If the patient's only disease is confined to a solitary lesion, its neoplastic nature must be confirmed by histology or cytology unless it is accompanied by GCIG criteria or can be clearly be shown as new disease when compared to prior imaging. ii) Disease in a previously irradiated field is acceptable as the only site of measurable disease only if there has been clear progression since completion of radiotherapy. * Age \> 18 years and competent to give informed consent. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2 and a life expectancy of at least 60 days. * Patients must have adequate: Bone marrow function: Absolute neutrophil count (ANC) greater than or equal to 1,500/ul, equivalent to Common Toxicity Criteria (CTCAE v4.0) grade 1. Platelets greater than or equal to 100,000/ul.; Renal function: creatinine less than or equal to 1.5 x institutional upper limit normal (ULN), CTCAE v4.0 grade 1.; Hepatic function: Bilirubin less than or equal to 1.5 x ULN (CTCAE v4.0 grade 1). serum glutamic oxaloacetic transaminase (SGOT) and alkaline phosphatase less than or equal to 2.5 x ULN (CTCAE v4.0 grade 1).; Neurologic function: Neuropathy (sensory and motor) less than or equal to CTCAE v4.0 grade 1.; No chemotherapy, radiotherapy, biologic, hormonal, or investigational drug therapy within 28 days prior to start of treatment on study. * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test prior to the study entry and be practicing an effective method of birth control during the course of the study, in a manner such that risk of failure is minimized. Prior to study enrollment, WOCBP must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an intentional pregnancy. * Phase 1A - Additional criteria applicable to phase 1A * Must have pathologically confirmed solid cancer that is locally advanced or metastatic cancer. * Patient's physician believes that the cancer is advanced, recurrent or metastatic and not curable by local measures (i.e., surgery, radiation, other drugs). * Patient's physician believes the patient may potentially benefit from this combination of therapy. * Patients may have had up to three (3) prior cytotoxic chemotherapeutic regimens including prior treatment with carboplatin and paclitaxel. Chemotherapy drug changes and modifications made for reasons other than progression are not considered a separate regimen. Examples would be drug changes for toxicity or consolidation chemotherapy after adjuvant treatment. Patients may have received any number of prior non-cytotoxic regimens such as monoclonal antibodies, cytokines, signal transduction inhibitors, or hormonal therapy. Previous radiation therapy is allowed. * Phase 1B - Endometrial: Additional Inclusion Criteria * Epithelial endometrial cancer. (i.e. carcinosarcoma, leiomyosarcoma, and endometrial stromal sarcoma are excluded). * May have had up to one prior chemotherapy for endometrial cancer. Prior taxane or platinum therapy is allowed as long as it was received either as adjuvant therapy or if there were a response to prior therapy and at least 6 months have elapsed since platinum treatment. Radiation sensitizing chemotherapy will not count as a prior regimen. * Must have measurable disease * Phase 1B - Ovarian: Additional Inclusion Criteria * Recurrent epithelial ovarian cancer (no stromal or germ cell ovarian cancers) * Platinum-sensitive defined as a recurrence at least 6 months (180 days) after the last day of primary adjuvant chemotherapy. Patients may have been retreated with a salvage line of chemotherapy but there must be a platinum-free interval of 6 or more months. * Two (2) or less prior therapies including adjuvant chemotherapy * Measurable or evaluable disease Exclusion Criteria: * An upper gastrointestinal or other condition that would impair swallowing or absorption of oral medication * Any serious illness or medical condition that would not permit the patient to be managed according to the protocol, including, but not limited to, any the following: * History of significant neurologic or psychiatric disorder (e.g., uncontrolled psychiatric disorders) that would impair the ability to obtain consent or limit compliance with study requirement * Active uncontrolled or serious infection * Active peptic ulcer disease * Patients who have the following cardiac conditions: Uncontrolled angina or myocardial infarction with the past six months; Diagnosed or suspected congenital long QT syndrome; Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes); Prolonged QTc interval on pre-entry electrocardiogram (\> 450 msec) on both the Fridericia and Bazett's correction * Uncontrolled hypertension defined as systolic greater than 180 and diastolic greater than 100. * History of other invasive malignancies in the last 3 years, with the exception of non-melanoma skin cancer, unless they have had no evidence of recurrence from that cancer for last two years. * Serum creatinine \>1.5 times the institutional upper limits of normal * Patients taking certain concomitant medications (see below). Patients can enroll on protocol if they stop these medications and a wash-out period of ≥14 days, unless otherwise noted, is done prior to starting ridaforolimus. * There must be at least 14 days since prior (and no current expectations to receive) CYP3A4 inhibitors including, but not limited to, any of the following: Azole antifungals ( i.e., ketoconazole, itraconazole, miconazole, fluconazole); HIV protease inhibitors (i.e., indinavir, saquinavir, ritonavir, atazanavir, nelfinavir); Clarithromycin; Verapamil; Erythromycin; Delavirdine; Diltiazem; Nefazodone; Telithromycin * There must be at least 14 days since prior (and no current expectations to receive) CYP3A4 inducers including, but not limited to, any of the following * Rifampin * Phenytoin * Rifabutin * St.John's wort * Carbamazepine * Efavirenz * Phenobarbital * Tipranavir * Full dose anticoagulation with warfarin (coumadin) or other vitamin K dependent anticoagulant. Low-dose prophylactic warfarin (i.e. 1mg per day port prophylaxis) is allowable. Low molecular heparin (e.g., danaparoid, dalteparin, tinzaparin, enoxaparin) is allowable if patient has been established on therapy. * Have received an estimated dose of radiation therapy to \>35% of the bone marrow. * Patients previously exposed to mTOR inhibitors are permitted in phase 1A but not allowed in phase 1B. * History of grade 3 hypersensitivity to paclitaxel. However, if after prior hypersensitivity the patient was subsequently successfully rechallenged without incident, the patient may be eligible at investigator's discretion. * Known hypersensitivity to the study drug ridaforolimus or its components. Ridaforolimus should be administered with caution to patients known to be hypersensitive to macrolide antibiotics, Tween80 (polysorbate 80), or any other excipient in the product formulation. * Significant lipid abnormalities: Serum cholesterol \> 350mg/dL; Triglycerides \> 400mg/dL