This is a phase I, open-label, study of BP1001-A in participants with advanced or recurrent solid tumors. The dose escalation phase will determine the safety and the maximum tolerated dose (MTD) or maximum administered dose (MAD) of BP1001-A as a single agent. After the MTD or MAD of BP1001-A is established, the dose expansion phase will commence and determine the safety, toxicity and response of BP1001-A in combination with paclitaxel.

Inclusion Criteria:

1. All participants, ≥ 18 years of age, with histologic evidence of advanced or recurrent solid tumors, who are not candidates for regimens or protocol treatments known to confer clinical benefit.

2. ECOG Performance Status Score of 0 or 1.

3. Participants must be willing to undergo pre-treatment biopsies. Participants who complete 1 cycle of treatment will undergo post-treatment biopsies. Post-treatment biopsies will be offered to participants who do not complete 1 cycle of treatment.

4. For the dose expansion phase, participants must have recurrent or persistent epithelial ovarian, primary peritoneal, fallopian tube or endometrial tumor and must be participants for whom single agent paclitaxel would be considered a reasonable treatment option.

5. Endometrial cancer patients with the following histologic epithelial cell types are eligible: Endometrioid adenocarcinoma, serous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, adenocarcinoma not otherwise specified, mucinous adenocarcinoma, squamous cell, transitional cell carcinoma, and mesonephric carcinoma.

   Ovarian tumor patients with the following histologic epithelial cell types are eligible: High-grade serous carcinoma, endometrioid carcinoma, clear cell carcinoma, squamous carcinoma, transitional cell (Brenner) carcinoma, mixed epithelial-stromal carcinoma, undifferentiated or other epithelial carcinoma.

   Uterine carcinosarcoma and other sarcomas of the uterus are not eligible.

6. Estimated life expectancy > 3 months in the Investigator's opinion.

7. All participants must have measurable disease per RECIST criteria v1.1. Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded). Each lesion must be >/= 20 mm when measured by conventional techniques, including plain x-ray, CT, and MRI, or >/= 10 mm when measured by spiral CT. Measurable disease lesions must be amenable to pre- and post-treatment biopsy.

8. Participants must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST v1.1. Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy.

9. Participants must have adequate:

   1. Bone marrow function: HgB >/= 9 g/dL, WBC >/= 3,000/mcL, ANC >/= 1,500/mcL, PLT >/= 100,000/mcL
   2. Hepatic function: Total bilirubin within normal institutional limits, AST and ALT < 2.5 X institutional ULN
   3. Renal function: Serum creatinine < 1.5 x ULN or eGFR > 60 mL/min according to Cockcroft-Gault formula
   4. Neurologic function: Neuropathy (sensory and motor) </= CTCAE Grade 1
   5. Blood coagulation parameters: PT such that INR is < 1.5 (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin or low molecular weight heparin) and a PTT < 1.2 times control

10. Participants previously treated with docetaxel (regardless of response) are eligible for this trial.

11. Participants in the dose expansion phase who previously received paclitaxel for primary or recurrent disease are eligible if they did not progress on therapy or relapse within 6 months of completing therapy. Participants with persistent disease at the completion of primary therapy with paclitaxel are not eligible.

12. Participants should be free of active infection requiring antibiotics, with the exception of uncomplicated UTI.

13. Any hormonal therapy directed at the malignant tumor must be discontinued at least two weeks prior to BP1001-A treatment. Continuation of hormone replacement therapy is permitted; stable regimens of hormonal therapy for prostate cancer (e.g., leuprolide, a gonadotropin-releasing hormone [GnRH] agonist), ovarian or breast cancer are not exclusionary.

14. Any other prior therapy directed at the malignant tumor, including immunologic agents, must be discontinued at least four weeks prior to first dose of BP1001-A (6 weeks for nitrosoureas or mitomycin C).

15. Female participants of childbearing potential must have a negative urine pregnancy test performed within 24 hours prior to the start of study treatment. Post-menopausal subjects (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test.

16. Female participants of childbearing potential must agree to use an acceptable method of birth control (i.e., a hormonal contraceptive, intrauterine device, diaphragm with spermicide, condom with spermicide or abstinence) for the duration of the study and for at least 6 months after the last dose of treatment.

17. Male participants must agree to use an acceptable method of contraception for the duration of the study.

18. Participants must be willing and able to provide written informed consent.

Exclusion Criteria:

1. For the dose expansion phase, participants must not have low grade serous ovarian carcinoma or mucinous ovarian carcinoma.
2. For the dose expansion phase, participants must wait at least two weeks after receiving any strong inhibitor, inducer, or substrate of both CYP3A4 and CYP2C8 before investigational drug administration.
3. Participants who had previous bone marrow or hematopoietic stem cell transplant.
4. Participants may not be receiving any other investigational agents.
5. Female participants who are pregnant or breast-feeding.
6. History or evidence upon physical examination of CNS disease, including primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack or subarachnoid hemorrhage within 6 months of registration on this study.
7. Within the past 6 months, participant has had any of the following: myocardial infarction, unstable angina pectoris, coronary/peripheral artery bypass graft, cerebrovascular accident, or transient ischemic attack.
8. Presence of concurrent conditions that, in the opinion of the Investigator and/or Medical Monitor, may compromise the participant's ability to tolerate study treatment or interfere with any aspect of study conduct or interpretation of results. This includes, but is not limited to, unstable or uncontrolled angina, NYHA class III or IV congestive heart failure, uncontrolled and sustained hypertension, clinically significant cardiac dysrhythmia, or clinically significant baseline ECG abnormality (e.g., QTcF >470 msec).
9. Active pleural effusion or pleural or pericardial effusion with symptoms. Pleural or pericardial effusion that has received treatment and resolved according to the Investigator, is acceptable.
10. Participants who are ineligible to undergo an MRI scan for reasons such as claustrophobia or the presence of implanted devices or metallic foreign bodies that are not MR compatible, such as ferromagnetic implants or pacers or with a known history of allergic reaction to gadolinium contrast agents.
11. Any condition which, in the Investigator's opinion, makes the subject unsuitable for trial participation.
12. A prior history of ≥ Grade 3 hypersensitivity to paclitaxel or docetaxel or with products mixed in Cremephor EL or Tween 80®.
13. Unresolved toxicity higher than CTCAE Grade 1 attributed to any prior therapy or procedure, excluding alopecia.
14. Substance abuse, medical, psychological, or social conditions that may interfere with the patient's participation in the study or evaluation of the study results.
15. Participants with HIV infection who have CD4+ T-cell counts < 350 cells/mcL or with clinically active hepatitis B or C infection.
16. Participants who have a major surgical procedure, open biopsy, dental extractions, or other dental surgery/procedure that results in an open wound, or significant traumatic injury within 28 days prior to the first date of treatment on this study, or anticipation of need for major surgical procedure during the course of the study; patients with placement of vascular access device or core biopsy within 7 days prior to registration.
17. (For dose expansion phase) Subjects ineligible or unable to receive paclitaxel as treatment for their disease.