A Study to Assess Adverse Events, Change in Disease Activity and How Intravenous (IV) ABBV901 Moves Through the Body Alone or in Combination With Other Anticancer Drugs in Adult Participants With 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.