Evaluating the Addition of OK-1 Weekly Paclitaxel in Patients With Endometrial Cancer

Inclusion Criteria: * At least 18 years-of-age at the time of signature of the informed consent form (ICF). * Histologically documented carcinoma of the endometrium, including endometrioid, serous, mixed adenocarcinoma, clear-cell carcinoma, or carcinosarcoma. Evidence that the endometrial cancer is advanced, recurrent, or persistent and has relapsed, or is refractory to curative therapy or established treatments. * Must have pre-treatment archival tissue. * Measurable disease by RECIST v1.1 is required for the phase 2 portion of the study. Patients with accessible disease are eligible for the safety lead in cohorts. Patients with biochemical recurrent disease only (ie Ca125 elevation or ctDNA elevation in absence of visible disease on CT scan are NOT eligible) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. * Patients 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. * Adequate organ function, defined in study protocol. * Prior therapy: Patients must have received ≥1 platinum-based therapy in the recurrent/metastatic setting and not more than 5 prior lines of therapies. * Adjuvant therapy given for early stage, high risk endometrial cancer does NOT count as the line of qualifying platinum based chemotherapy unless disease recurrence is documented \< 12 months from completion. If \>12 months has elapsed, patients should receive another line of platinum based chemotherapy. * Maintenance therapy (e.g., bevacizumab, poly adenosine diphosphate-ribose polymerase \[PARP\] inhibitor, endocrine therapy or immune checkpoint inhibitor will be considered part of the preceding line of therapy. * Therapy changed due to toxicity in the absence of progression will be considered part of the same line (i.e., not counted independently) * Hormonal therapy will not be counted as a separate line of therapy. * Patients should have received an immune checkpoint inhibitor as part of a prior line of therapy unless contraindicated to participate in this trial. * If the Patient has a tumor that is HER2 3+, trastuzumab deruxtecan should have been used unless ineligible. * During the course of this clinical trial, if an antibody drug conjugate becomes available therapy for recurrent endometrial cancer, patients should be treated with that therapy unless ineligible * The patient must provide study-specific informed consent prior to study entry and, for patients treated in the U.S., authorization permitting release of personal health information. * QTcF \< 470 msec Exclusion Criteria: * Patients who have received prior weekly paclitaxel for recurrent endometrial cancer. * Major surgical procedure within 28 days prior to registration, or anticipation of need for major surgical procedure during the study. Note: Placement of a vascular access device, thoracentesis, and/or paracentesis will not be considered major surgery. * Women who are pregnant or are unwilling to discontinue nursing. * Evidence of bleeding diathesis or clinically significant coagulopathy within the past 3 months. Patients are not excluded for past or current use of anticoagulation. * There is no prespecified washout from prior therapies. * Patients with adverse events related to prior therapies must have resolution to \< grade 1. Patients with ≤ Grade 2 neuropathy or ≤ Grade 2 alopecia are an exception to this criterion and may qualify for the study. Note: Grade 2 neuropathy is neuropathy on one medication so patients may be eligible following discussions with the medical monitor. Additional exceptions include immune-related AEs such as adrenal insufficiency, hypothyroidism (controlled), endocrine-related toxicities due to checkpoint inhibitor treatment (can be corrected through hormone replacement therapy) and Grade 2 laboratory abnormalities that meet the eligibility requirements. * Patients currently taking and unwilling/unable to discontinue the use of drugs that are known to be strong/moderate inhibitors or inducers of CYP3A4, CYP2C8, CYP2C19, and CYP2C9. (Refer to Appendix III) * Comorbid Conditions: No active infection requiring parental antibiotics except for urinary tract infection. * No evidence of intra-abdominal abscess, abdominal/pelvic fistula, gastrointestinal perforation, or GI obstruction requiring gastrostomy tube. NOTE: required interval since last bowel obstruction: 30-day minimum for incomplete obstruction, resolved with conservative means; 6 months for fistula. Patients with a history of a large bowel obstruction that has been successfully diverted and do not meet the criteria for small bowel obstruction are eligible. * Patients with risk factors for torsade de pointes (TdP) such as clinically significant heart failure (defined as a known ejection fraction \< 50%), uncorrected grade 2 or greater hypokalemia, family history of long QT syndrome )