DT2216 + Paclitaxel in Platinum-Resistant Ovarian Cancer

Inclusion Criteria: * Participants must have histologically confirmed relapsed or refractory ovarian cancer (including epithelial ovarian cancer, fallopian tube carcinoma, or primary peritoneal carcinoma). * Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non- nodal lesions and short axis for nodal lesions) as ≥20 mm (≥2 cm) by chest x-ray or as ≥10 mm (≥1 cm) with CT scan, MRI, or calipers by clinical exam. * Participants must have received at least one prior platinum-based chemotherapeutic regimen for primary management of disease. * Participants must have been treated with at least one line of standard-of-care platinum-based chemotherapy but otherwise there is no limit on lines of prior systemic therapy. For participants who received recent palliative radiotherapy, the radiation treatment must have been completed at least two weeks prior to initiating study treatment. Prior dose-dense paclitaxel as part of initial treatment and prior treatment with weekly paclitaxel in the recurrent setting is permitted; however, at least 6 months must have elapsed between the last dose of weekly paclitaxel and protocol treatment initiation. * Age ≥18 years. * ECOG performance status 0-2. * Participants must meet the following laboratory criteria: * absolute neutrophil count ≥1000/mcL\* * platelets ≥100,000/mcL\* * hemoglobin ≥8 g/dL * total bilirubin ≤ 1.5x institutional upper limit of normal (ULN)\*\* * AST(SGOT)/ALT(SGPT) ≤3x institutional ULN\*\*\* * PT/INR ≤ 1.5xinstitutional ULN * Serum albumin ≥ 3.0 g/dL * eGFR (glomerular filtration rate) ≥50 mL/min\*\*\*\* * Hematologic criteria must be met in the absence of platelet transfusion within 3 days prior to the screening laboratory measurements. Criteria must also be met without G-CSF products for two weeks and romiplostim for four weeks prior to screening. * In patients with Gilbert's disease, total bilirubin should be ≤ 4.0x ULN --\*\*\*In patients with documented hepatic involvement, ≤ 5.0x ULN --\*\*\*\*Unless patient is receiving anticoagulant therapy and the PT/INR or aPTT is within the intended therapeutic range of the anticoagulant. * eGFR should be calculated using the 2021 chronic kidney disease epidemiology (CΚD-EPI) creatinine equation (preferred) or other formula. To convert to units of mL/min from units of mL/minute/1.73 m2, multiply the estimated GFR by the individual's body surface area and divide by 1.73. * Participants with known HIV infection should meet the following criteria: * CD4+ count ≥ 300/μL. * Undetectable viral load * Receiving highly active antiretroviral therapy * No history of AIDS-defining opportunistic infection in the past 12 months * Participants with past Hepatitis B or C infections must have been treated appropriately and have undetectable virus levels in the plasma. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. Patients with a previously treated malignancy are eligible if all treatment of that malignancy was completed at least 2 years before registration and the patient has no evidence of disease. Patients who have a concurrent malignancy that is clinically stable and does not require tumor-directed treatment are allowed to participate. * Participants must have platinum-resistant disease, defined by disease progression within 6 months (i.e., 183 days) from their last dose of prior platinum chemotherapy. Disease progression may be defined by imaging or by clinical progression per the assessment of the treating oncologist. * Participants must have epithelial ovarian cancer of any histology. * The effects of DT2216 on the developing human fetus are unknown. For this reason and because paclitaxel is known to be teratogenic, females of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence from penile-vaginal intercourse) prior to study entry and for the duration of study participation. Participants of childbearing potential who elect to use barrier methods should use a second form of contraception (e.g., cervical cap or diaphragm + male condom, or male condom + vaginal spermicide, etc.) given the failure rates of barrier methods and potential risks to the fetus of the study drugs. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Participants of child-bearing potential should agree to continue to use adequate contraception for at least 3 months after the last dose of study drug. * The participant or the participant's legal representative must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Prior treatment with any BCL-XL inhibitor, such as navitoclax. * Participants who are receiving any other investigational agents for this condition or received an investigational agent within 5 half-lives of the agent or 4 weeks, whichever is shorter. * Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> Grade 1) except for alopecia. Participants with endocrine- related AEs who are adequately treated with hormone replacement or participants who have grade 2 neuropathy are eligible. Participants with grade 2 anemia likely related to prior treatment are eligible. Participants with a history of a thromboembolic event who are on stable therapeutic anticoagulation are eligible. Participants with asymptomatic grade 2 hypertension controlled with anti-hypertensive medications are eligible. * Ongoing treatment with chronic immunosuppressants or systemic steroids \> 10