Inclusion

          -  Has read and understands the informed consent form (ICF) and has given written IC
             prior to any study specific procedures.

          -  Histologic or cytologic diagnosis of epithelial ovarian, fallopian tube, or primary
             peritoneal cancer.

          -  Progressed within 6 months of completing at least 4 cycles of a first-line
             platinum-containing regimen for Stage III/IV disease. Patients with refractory disease
             (progression during platinum-containing therapy) are ineligible.

          -  No more than 2-4 prior treatment regimens for Stage III/IV disease, defined as
             investigational, chemotherapy, hormonal, biologic, or targeted therapy.

          -  Prior doxorubicin (or other anthracycline) at a cumulative dose of ≤ 360 mg/m² or
             cumulative epirubicin dose of ≤ 720 mg/m² (calculated using doxorubicin equivalent
             doses: 1 mg of doxorubicin = 1 mg PLD = 0.3 mg mitoxantrone = 0.25 mg idarubicin).
             Subjects without any prior anthracycline exposure can also be included. Applies to Arm
             D only.

          -  At least 1 measurable lesion according to RECIST v1.1.

          -  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.

          -  Baseline Laboratory Values:

               1. ANC ≥1500/μL

               2. HgB ≥ 9 g/dL with no blood transfusions in the past 28 days

               3. Platelets ≥ 100,000/μL

               4. ALT & AST ≤3 x ULN or ≤5 x ULN if known hepatic metastases

               5. Serum bilirubin within normal limits (WNL) or ≤1.5 x the ULN in patients with
                  liver metastases; or total bilirubin ≤3.0 x ULN with direct bilirubin WNL in
                  patients with well documented Gilbert's Syndrome.

               6. Serum creatinine ≤1.5 x the ULN and a calculated creatinine clearance (CrCl) ≥45
                  mL/min by the Cockcroft-Gault method.

          -  Left ventricular ejection fraction (LVEF) WNL of the institution as determined by
             multiple uptake gated acquisition (MUGA) or echocardiography (ECHO) (applies to Arm D
             only).

          -  Female patients, ≥18, (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 72
             hours prior to start.

          -  Predicted life expectancy ≥ 12 weeks

        Exclusion

          -  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 study treatment is required.

          -  Major surgical procedures ≤ 28 days of beginning study, or minor surgical procedures ≤
             7 days. No waiting period following port-a-cath placement, or any other central venous
             access placement.

          -  Grade >1 toxicity from prior therapy (except alopecia or anorexia).

          -  Known malignant CNS disease other than neurologically stable, treated brain
             metastases, defined as metastasis having no evidence of progression or haemorrhage
             after treatment for at least 2 weeks (including brain radiotherapy). Must be off any
             systemic corticosteroids for the treatment of brain metastases for at least 14 days
             prior to enrolment.

          -  Patient has had prescription or non-prescription drugs or other products (i.e.
             grapefruit juice) known to be sensitive CYP3A4 substrates or CYP3A4 substrates with a
             narrow therapeutic index, or to be moderate to strong inhibitors or inducers of CYP3A4
             which cannot be discontinued 2 weeks prior to Day 1 of dosing and withheld throughout
             the study until 2 weeks after last dose of study drug.

          -  Caution should be exercised when inhibitors or substrates of P-gP, substrates of
             CYP1A2 with a narrow therapeutic range, sensitive substrates of CYP2C19 or CYP2C19
             substrates with a narrow therapeutic range are administered with adavosertib.

          -  Herbal medications should be discontinued 7 days prior to the first dose of study
             treatment.

          -  Any of the following cardiac diseases currently or within the last 6 months as defined
             by New York Heart Association (NYHA) ≥ Class 2:

               1. Unstable angina pectoris

               2. Congestive heart failure

               3. Acute myocardial infarction

               4. Conduction abnormality not controlled with pacemaker or medication

               5. Significant ventricular or supraventricular arrhythmias (patients with chronic
                  rate controlled atrial fibrillation in the absence of other cardiac abnormalities
                  are eligible).

          -  Adavosertib should not be given to patients who have a history of Torsades de pointes
             unless all risk factors that contributed to Torsades have been corrected. Adavosertib
             has not been studied in patients with ventricular arrhythmias or recent myocardial
             infarction.

          -  Corrected QT interval (QTc) >470 msec at study entry or congenital long QT syndrome.

          -  Pregnant or lactating.

          -  Serious active infection at the time of enrolment, or another serious underlying
             medical condition that would impair the patient's ability to receive study treatment.

          -  Presence of other active cancers, or history of treatment for invasive cancer within 3
             years. Patients with Stage I cancer who have received definitive local treatment
             within 3 years, and whom are considered unlikely to recur, are eligible. Patients with
             previously treated in-situ carcinoma (i.e., non-invasive) are eligible, as are
             patients with prior non-melanoma skin cancers.