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

Ovarian cancer (OC) is a lethal disease. The purpose of this study is to assess the safety, pharmacokinetics and efficacy of ABBV901, alone or in combination with other anticancer drugs, in participants with ovarian cancer. ABBV901 is an investigational drug for the treatment of ovarian cancer. This study has 6 parts where participants will receive ABBV-901, alone or in combination with other anticancer therapies. Around 285 participants will be enrolled in the study at approximately 45 sites around the world. In part 1, participants will receive escalating doses of intravenous (IV) ABBV-901 alone. In part 2, participants will receive 1 of 3 doses of IV ABBV-901 alone to determine the optimized dose. In part 3, participants will receive escalating doses of IV ABBV-901 in combination with IV bevacizumab. In part 4, participants will receive recommended doses for expansion of IV ABBV-901 combination with IV bevacizumab. in Part 5, participants will receive escalating doses of IV ABBV-901 in combination with IV carboplatin and IV bevacizumab and in part 6, participants will receive recommended doses for expansion of IV ABBV-901 combination with IV carboplatin and IV bevacizumab. The total study duration will be approximately 3 years. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic and may require frequent medical assessments, blood tests, and scans.

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 \