ONC201 Plus Weekly Paclitaxel in Patients With Platinum Refractory or Resistant Ovarian Cancer

Inclusion Criteria: * Histologic diagnosis of epithelial ovarian, fallopian tube, or primary peritoneal cancer. * Progressed within 6 months of completing at least 1 cycle of last platinum containing regimen. Patients with refractory disease (progression during platinum-containing therapy) are eligible. This includes both adjuvant therapy and in the recurrent setting. * No more than 4 prior treatment regimens defined as investigational, chemotherapy, hormonal, biologic, or targeted therapy in the platinum resistant setting and total of 7 prior regimens in all settings will be allowed. Prior maintenance therapy with biologic or targeted agent does NOT count as a treatment regimen (e.g. Maintenance bevacizumab, Parpi, or immunotherapy). * At least one measurable lesion according to RECIST v1.1. * For the eight patients enrolled for PK/PD. Availability of tissue from carcinoma. For most patients this will be archival tissue. If there is no archival tissue available, biopsy of lesion MUST be performed prior to initiation of therapy. Lesions must be available for biopsy as well in these patients. * Any prior palliative radiation therapy must be completed at least 7 days prior to start of study treatment and patients must have recovered from any acute adverse effects prior to start of study treatment. * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) score of 0-1. * Female patients who are not of childbearing potential and fertile female patients of childbearing potential who agree to use adequate contraceptive measures from 2 weeks prior to the study and until 1 month after study treatment discontinuation, who are not breastfeeding, and who have a negative serum or urine pregnancy test within 3 days prior to start of study treatment. * Patients must have adequate (at baseline): 1. Bone marrow function: Absolute neutrophil count (ANC) ≥1,500/µL. Platelets ≥100,000/µL and hemoglobin \> 8.0 gm/dL, transfusion allowed up to 1 week prior to maintain Hgb \>8. 2. Renal function: Calculated creatinine clearance (CrCl) ≥35 mL/min/1.73 mm2 3. Hepatic function: Bilirubin less than or equal to 1.5 x ULN; alkaline phosphatase (AP), aspartate transaminase (AST) and alanine transaminase (ALT) less than or equal to 3 x ULN. AP, AST and ALT less than or equal to 5 x ULN is acceptable if patient has known hepatic metastasis Exclusion Criteria: * Use of a study drug (approved or investigational drug therapy) ≤21 days or 5 half-lives (whichever is shorter) prior to the first dose of study treatment. For study drugs for which 5 half-lives is ≤21 days, a minimum of 10 days between termination of the study drug and administration of current study treatment is required. * Major surgical procedures ≤21 days of beginning study treatment, or minor surgical procedures ≤7 days. No waiting required following port-a-cath placement, ureteral stent placement, percutaneous nephrostomy tube placement. * No other (chemotherapy, immunotherapy, hormonal anti-cancer therapy, radiotherapy \[except for palliative local radiotherapy\]), biological therapy or other novel agent is to be permitted while the patient is receiving study medications * Grade \>1 toxicity from prior therapy (except alopecia or anorexia or above hematologic criteria) unless controlled by medications. * Inability to swallow oral medication. Note: Patient may not have a percutaneous endoscopic gastrostomy (PEG) tube or be receiving total parenteral nutrition (TPN) on this trial. * Known malignant central nervous system disease other than neurologically stable, treated brain metastases - defined as metastasis having no evidence of progression after treatment for at least 4 weeks (including brain radiotherapy). Must be off any systemic corticosteroids for the treatment of brain metastases for at least 14 days prior to enrollment. * Patient has had prescription or non-prescription drugs or other products (i.e. grapefruit juice) known to be moderate to strong inhibitors or inducers of CYP3A4, which cannot be discontinued 1 week prior to Day 1 of dosing and withheld throughout the study until 1 weeks after the last dose of study drug. * Any known hypersensitivity or contraindication to the components of study treatment * Pregnant or lactating * Serious active infection at the time of enrollment, or another serious underlying medical condition at discretion of the enrolling physician that would impair the ability of the patient to receive study treatment. HIV or other immunodeficiency disease that is well controlled and that does not impact baseline lab values (i.e. outside of above noted parameters for inclusion) are NOT considered exclusion criteria. * Presence of other active cancers other than ovarian cancer except those that do not require active therapy (i.e. on surveillance) and known non-invasive cancers and in situ cancers (e.g. non-melanoma skin cancers). * Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol.