This Phase I trial combines ADI-PEG 20 with docetaxel in patients with advanced solid tumors with emphasis on castration resistant prostate cancer (CRPC). The investigators hypothesize that the combination will result in greater tumor cytotoxicity with an acceptable toxicity profile (i.e., manageable side effects) in cancer patients due to the unique mechanism of action of ADI-PEG 20. The investigators also hypothesize that the combination of ADI-PEG 20 and docetaxel will result in enhanced tumor cell apoptosis in part due to autophagy and that this will be particularly relevant in CRPC.

Inclusion Criteria: (Dose-Escalation Phase)

1. For the dose-escalation phase, patients must have cytologically or histologically proven advanced malignant solid tumors, with emphasis on CRPC.
2. Patients must be 18 years of age or older.
3. Patients must have a Zubrod (ECOG) performance status of 0-2.
4. Patients must have an estimated survival of at least 3 months.
5. Any prior chemotherapy must have been completed at least 4 weeks prior to start of treatment. Prior radiation must have been completed at least 2 weeks prior to start of therapy. Patients must have recovered from acute reversible side effects of prior chemotherapy regimens or radiotherapy to < grade 1 (excluding alopecia, lymphopenia, and hyperglycemia) according to the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE), version 4.0.
6. Radiographs (Xrays, CT scans, etc) to follow disease response or progression must have been completed within 28 days prior to registration.
7. Patients must have adequate renal function as documented by a calculated creatinine clearance of > 45 ml/min (see Appendix for formula for calculating creatinine clearance).
8. Patients must have adequate liver functions: AST and ALT < 2.5 X upper limit of normal, and bilirubin < upper limit of normal.

Inclusion Criteria: MTD Expansion Phase Cohort 1 - CRPC

1. All patients must have a histologic diagnosis of adenocarcinoma of the prostate which is measurable or non-measurable.

2. Patients must have metastatic prostate cancer deemed to be unresponsive or refractory to hormone therapy by one or more of the following (despite androgen deprivation and antiandrogen withdrawal when applicable):

   • Progression of measurable disease assessed within 28 days prior to registration.
   • Progression of non-measurable disease assessed within 28 days prior to registration.
   • Rising PSA - Rising PSA is defined as at least two consecutive rises in PSA to be documented over a reference value (measure 1). The first rising PSA (measure 2) must be taken at least 7 days after the reference value. A third confirmatory PSA measure is required (2nd beyond the reference level) to be greater than the second measure, and it must be obtained at least 7 days after the 2nd measure. If this is not the case, a fourth PSA is required to be taken and be greater than the second measure. The patient must have a PSA ≥ 5 ng/ml in addition to increasing PSA to be eligible by rising PSA criteria alone. However, no minimum PSA is required for patients whose progression is based on measurable or non-measurable disease.

3. All patients must have a pre-study PSA obtained within 28 days prior to registration.

4. All patients must have had imaging studies within 28 days prior to registration. The choice of imaging studies to follow disease will be at the discretion of the investigator.

5. Patients must be offered the opportunity to participate in specimen banking for future use (to include the serum and tissue correlative studies).

6. Patients must have been surgically or medically castrated. If method of castration is LHRH agonists (leuprolide or goserelin) or LHRH antagonists, then the patient should be willing to continue the use of LHRH agonists. Patients who have stopped treatment should be willing to restart.

7. If the patient has been treated with non-steroidal antiandrogens (flutamide, bicalutamide, nilutamide or ketoconazole), they must have been stopped at least 14 days prior to registration for ketoconazole and at least 28 days prior to registration for flutamide, bicalutamide or nilutamide and the patients must have demonstrated progression.

8. Prior, planned, or ongoing bisphosphonate therapy or denosumab is allowed.

Exclusion Criteria:

(Dose-Escalation Phase)

1. Pregnant or breastfeeding women. The effects of these drugs on the unborn fetus are unknown. Documentation of a negative serum pregnancy test is required for all women of reproductive potential.
2. Patient has a clinically significant concurrent illness. Patients must not have a serious intercurrent medical or psychiatric illness, including serious active infection.
3. Patient is currently enrolled in a different clinical study in which investigational procedures are performed or investigational therapies are administered. Also, a patient may not enroll in such clinical trials while participating in this study.
4. Patient has a history of allergy or hypersensitivity to the study drugs or a taxane.
5. Patient has serious medical risk factors involving any of the major organ systems such that the investigator considers it unsafe for the patient to receive an experimental research drug.
6. Prior therapy with ADI-PEG 20 or docetaxel.
7. Allergy to pegylated compounds or study drugs.

Exclusion Criteria: MTD Expansion Phase Cohort 1 - CRPC

1. Patient has a clinically significant concurrent illness. Patients must not have a serious intercurrent medical or psychiatric illness, including serious active infection.
2. Patient is currently enrolled in a different clinical study in which investigational procedures are performed or investigational therapies are administered. Also, a patient may not enroll in such clinical trials while participating in this study.
3. Patient has a history of allergy or hypersensitivity to the study drug or a taxane.
4. Patient has serious medical risk factors involving any of the major organ systems such that the investigator considers it unsafe for the patient to receive an experimental research drug.
5. Prior therapy with ADI-PEG 20 or docetaxel.
6. Allergy to pegylated compounds.