A Study of DKN-01 as a Monotherapy or in Combination With Paclitaxel in Patients With Recurrent Epithelial Endometrial or Epithelial Ovarian Cancer or Carcinosarcoma

Inclusion Criteria: 1. Diagnosis: 1. Epithelial Endometrial Cancer: histologically confirmed diagnosis (by either primary surgical specimen or biopsy for recurrence) of recurrent previously treated EEC. 2. Epithelial Ovarian Cancer: histologically confirmed diagnosis (by either primary surgical specimen or biopsy for recurrence) of recurrent platinum-resistant/refractory EOC, primary peritoneal, or fallopian tube cancer (i.e., disease recurrence within 6 months of completion of or progression during platinum-based chemotherapy). 3. Carcinosarcoma/Malignant Mixed Mullerian Tumors: histologically confirmed diagnosis (by either primary surgical specimen or biopsy for recurrence) of recurrent uterine or ovarian carcinosarcoma (MMMT). Patients must have had only 1 prior chemotherapeutic regimen for management of carcinosarcoma that may have been included chemotherapy (including in adjuvant setting), chemotherapy and radiotherapy, and/or consolidation/maintenance therapy. 2. Refractory or intolerant to at least one prior standard therapy(ies) for metastatic or locally advanced disease (see Inclusion Criterion #1c for Groups 5-6). 1. If prior therapy consisted of palliative chemoradiation therapy, it will be considered one line of therapy. 2. Prior treatment with paclitaxel as part of definitive therapy regimen is acceptable, provided the patient is not intolerant of paclitaxel. 3. Patients who are not eligible to receive paclitaxel will be allowed to receive single agent DKN-01. 3. Tumor tissue for mandatory pre-treatment and on-treatment biopsies. 4. One or more tumors measurable on radiographic imaging as defined by RECIST 1.1. 5. Ambulatory and ≥18 years of age. 6. ECOG performance status (PS) of 0 or 1 a. ECOG PS of 2 may be eligible upon the review and approval of the Medical Monitor. 7. Estimated life expectancy of at least 3 months, in the judgment of the Investigator. 8. Disease-free of active second/secondary or prior malignancies for ≥2 years with the exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or breast. 9. Acceptable liver, renal, hematologic and coagulation function 10. Females of child bearing potential and male partners of female patients must agree to use adequate contraception during the study and for 6 months after their last dose of study drug. 11. Reliable and willing to make themselves available for the duration of the study and are willing to follow study-specific procedures. 12. Provided written informed consent prior to any study-specific procedures. Exclusion Criteria: 1. Patients with the following pure histologies of endometrial or ovarian cancer are not eligible for enrollment: germ cell, sex cord stroma, or sarcoma. 2. New York Heart Association Class III or IV cardiac disease, myocardial infarction within the past 6 months, or unstable arrhythmia. 3. Fridericia-corrected QT interval (QTcF) \> 470 msec (female) or history of congenital long QT syndrome. 4. Active, uncontrolled bacterial, viral, or fungal infections, within 7 days of study entry requiring systemic therapy. 5. Known to be human immunodeficiency virus (HIV) positive, have hepatitis B surface antigen (HBSAg), or hepatitis C antibodies (HCAb), unless hepatitis C virus ribonucleic acid (HCV RNA) undetected/negative. 6. History of major organ transplant (i.e., heart, lungs, liver, or kidney). 7. History of autologous/allogenic bone marrow transplant. 8. Serious nonmalignant disease 9. Pregnant or nursing. 10. History of osteonecrosis of the hip or have evidence of structural bone abnormalities in the proximal femur on MRI scan that are symptomatic and clinically significant. 11. Symptomatic central nervous system (CNS) malignancy or metastasis. 12. Known osteoblastic bony metastasis 13. Treatment with surgery or chemotherapy within 21 days prior to study entry (42 days for nitrosoureas or mitomycin C) 14. Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to study entry. 15. Clinically significant peripheral neuropathy at the time of study entry. Patients with pre-existing peripheral neuropathy will be allowed to receive single agent DKN-01 16. History of hypersensitivity reactions to paclitaxel or other drugs formulated in Cremophor® EL (polyoxyethylated castor oil). Patients who exhibit these hypersensitivities will be eligible to receive single agent DKN-01 17. Prior radiation therapy within 14 days prior to study entry 18. Currently receiving any other investigational agent or received an investigational agent within last 30 days of study entry. 19. Previously treated with an anti-DKK1 therapy 20. Significant allergy to a pharmaceutical therapy that, in the opinion of the Investigator, poses an increased risk to the patient 21. Active substance abuse