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 weekly paclitaxel in the recurrent setting. Prior dose-dense paclitaxel as part of the initial treatment at diagnosis is allowed. * 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 mg of prednisone daily (or equivalent). 10 mg daily of oral prednisone or less can be continued if clinically required. * Known active central nervous system involvement with metastatic cancer, including leptomeningeal disease. Participants with previously treated brain metastases may enroll if the disease is stable for at least one month on imaging with no neurologic symptoms and participants are not receiving pharmacologic doses of glucocorticoids for this diagnosis. * Prior organ transplantation or other cellular therapies such as Chimeric Antigen Receptor T-cells. Prior allogeneic stem cell transplantation (SCT) is allowed if there is no evidence of Graft Versus Host Disease and if participant meets other eligibility criteria listed. Prior autologous SCT is permitted if the participant meets the other eligibility criteria listed. * History of major surgery within 8 weeks prior to first dose of study drug. * History of clinically significant small or large bowel obstruction within 8 weeks prior to first dose of study drug (e.g. symptomatic, impairing nutrition, requiring nasogastric tube, requiring hospital admission). * History of clinically significant ascites or pleural effusion requiring recurrent paracentesis or thoracentesis within 4 weeks prior to first dose of study drug. * Dependence upon TPN or regular IV fluid resuscitation. * History (≤2 weeks before the start of treatment with the study drug) of ongoing or active infections (Grade ≥ 2). * Baseline prolongation of QTc interval (\> 470 msec) using Bazett's formula or history of Long QT Syndrome. Caution should be exercised with the use of concomitant medications that prolong the QTc interval. * History of a bleeding complication within the past 4 weeks, or a clinically significant bleeding predisposition. * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, symptomatic angina pectoris, cardiac arrhythmia, on dialysis, on any organ transplant list; any medical condition for which the primary oncologist or principal investigator deems the participant an unsuitable candidate to receive DT2216 and/or paclitaxel; or psychiatric illness or other situations that would limit compliance with study requirements. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to DT2216 or paclitaxel. Participants with known allergy or hypersensitivity to paclitaxel or to its vehicle formulation may not enroll, except participants who have subsequently tolerated paclitaxel infusions after a hypersensitivity reaction with or without modifications to the pre-medications. If participants develop allergy or hypersensitivity to paclitaxel during treatment on the study, they may be able to remain on study via receiving paclitaxel with a desensitization procedure supervised by an allergy physician after a formal allergy consultation and discussion with the study PI. * Participants receiving any medications or substances that are strong inhibitors or inducers of the cytochrome P450 isoenzyme CYP3A4 or CYP2C8 are ineligible. Strong CYP3A4 or CYP2C8 inhibitors and inducers should be discontinued at least 2 weeks prior to the first dose of DT2216. As per paclitaxel product documentation, it is important to use caution with known substrates or inhibitors of the cytochrome P450 isoenzymes CYP3A4 and CYP2C8. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference. As part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product. * Pregnant females are excluded from this study because the effects of DT2216 on the developing fetus are unknown. Participants must have a negative pregnancy test result at screening (for females of childbearing potential). The test must be performed at the screening and Cycle 1 Day 1 visits. Participants of non-childbearing potential will have had at least continuous 12 months of natural (spontaneous) amenorrhea, and an appropriate clinical profile (e.g., age appropriate, history of vasomotor symptoms), or have had surgical bilateral oophorectomy, hysterectomy, or have had bilateral tubal ligation \>6 weeks prior to screening. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with DT2216, breastfeeding should be discontinued if the mother is treated with DT2216. These potential risks may also apply to other agents used in this study; specifically, paclitaxel has known embryo- and fetotoxicity.