ABBV901 for Advanced Ovarian Cancer

Inclusion Criteria: * Diagnosis of an advanced or unresectable malignant high grade serous epithelial ovarian, fallopian tube, and primary peritoneal cancers (EOC), fallopian tube or primary peritoneal cancer by histology (World Health Organization \[WHO\] criteria). * Participants enrolled in backfill (Part 1) must provide consent to paired fresh biopsies which are pretreatment and on-treatment tumor biopsies from the same tumor lesion. For Parts 1-4: \- Participants must be considered platinum resistant or platinum ineligible. Platinum resistant disease is defined as radiographic progression within 6 months (up to 182 days) after the last dose of the most recent platinum therapy). For Parts 5-6: \- Participants will have platinum-sensitive disease defined as radiographic progression \> 6 months from last dose of platinum-based chemotherapy. Note: Progression should be calculated from the date of the last administered dose of platinum therapy to the date of the radiographic imaging showing progression. Exclusion Criteria: * Ovarian Cancer (OC) with histologies other than high grade serous OC including endometrioid, low grade, mucinous, carcinosarcoma or sarcomatous histology, mixed tumors or low grade/borderline ovarian tumor. * Participants with platinum refractory disease. * Prior therapy with an antibody-drug conjugate containing a topoisomerase inhibitor. * Prior history of Grade \>= 2 interstitial lung disease (ILD) or pneumonitis. * Prior history of Grade 2 \>= 2 ILD or pneumonitis or any evidence of active ILD or pneumonitis on Screening chest computed tomography (CT) scan. For Parts 3-6: * History of Grade 3/4 adverse events that, in the opinion of the investigator, are attributed to bevacizumab. * History of clinically significant cardiac disease including CHF Class II or higher NYHA; active coronary artery disease, MI within 6 months prior to study entry; unevaluated new onset angina within 3 months or unstable angina (angina symptoms at rest) or cardiac arrhythmias requiring antiarrhythmic therapy (beta blockers or digoxin are permitted). * Echocardiogram with ejection fraction \<= 50% and no other clinically significant cardiac abnormalities that in the opinion of the investigator, would increase the participants susceptibility to cardiac toxicity. For Parts 5-6: \- Participants who had prior allergic reaction to platinum containing compound.