Inclusion Criteria:

• Histologically or cytologically confirmed ovarian epithelial cancer.
• Evidence of progressive disease (PD) on or within 6 months of a platinum (cisplatin or carboplatin) regimen: at least 1 prior regimen must have contained a platinum-taxane combination.
• Measurable disease as defined by RECIST 1.1.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• Fresh or archived tumor tissue sample available for target expression analysis. [Phase 1b only: Subjects' tumor tissue must test positive for target expression.].
• Adequate hematologic and organ function as confirmed by laboratory values.
• At least 3 weeks between last systemic chemotherapy and planned start of study treatment (4 weeks for prior investigational drugs or biologics) for ovarian cancer.
• At least 3 weeks between major surgery and planned start of study treatment; major incisions must have healed.

Exclusion Criteria:

• History of prior malignancy, with the exception of the following: malignancy treated with curative intent and with no evidence of active disease present for more than 3 years prior to screening and felt to be at low risk for recurrence by treating physician; or adequately treated lentigo maligna melanoma without current evidence of disease or adequately controlled non-melanomatous skin cancer; or adequately treated cervical carcinoma in situ without current evidence of disease.
• Uncontrolled infection requiring systemic antibiotics/antivirals/antifungals.
• Evidence of complete or partial bowel obstruction.
• Patients requiring IV hydration or parenteral nutrition.
• Positive pregnancy test in females of child-bearing potential or pregnant or currently breastfeeding.
• Known hypersensitivity to any component of study drug including potential subjects with a history of major immunologic reaction to any IgG-containing agent.
• Inability to tolerate premedication with dexamethasone.
• Uncontrolled cardiac disease, or myocardial infarction within the last 12 months, or left ventricular ejection fraction (LVEF) < 50%, or QTcF interval > 470 msec.
• Class II, III or IV heart failure as defined by the NYHA functional class system.
• Positive serology for hepatitis B or C, or known human immunodeficiency virus infection (HIV).
• Previous treatment with a pyrrolobenzodiazepine (PBD)-based drug.

Additional exclusion criteria for the SC-003 and ABBV-181 combination treatment regimen:

• History of inflammatory bowel disease.
• Active autoimmune disease, with exceptions of psoriasis not requiring systemic treatment, vitiligo, type 1 diabetes mellitus and hypothyroidism.
• History of primary immunodeficiency, allogeneic bone marrow transplantation, solid organ transplantation, or previous clinical diagnosis of tuberculosis.
• History of immune-mediated pneumonitis.
• Current or prior use of immunosuppressive medication within 14 days prior to the first dose of study treatment.