Phase I Study of Docetaxel and 177-Lutetium-PSMA-I&T in First-Line Treatment for Patients With Metastatic Castration-Resistant Prostate Adenocarcinoma

Inclusion Criteria: 1. Men aged 18 years or older. 2. Histological or cytological diagnosis of prostate adenocarcinoma. The presence of intraductal or cribriform carcinoma will be allowed. 3. Presence of metastatic disease on conventional imaging exams (bone scintigraphy and/or CT scan or MRI). 4. Patients with castration-resistant disease, defined as testosterone \<50 ng/mL in the context of prior orchiectomy or ongoing androgen deprivation therapy (ADT) with LHRH agonists or antagonists, plus at least one of the criteria below: 5. PSA ≥2.0 ng/mL with at least two consecutive PSA rises at intervals of at least 1 week. 6. Radiologic progression defined by the investigator. 7. Clinical progression defined by the investigator. 8. Performance status per the Eastern Cooperative Oncology Group (ECOG) equal to 0 or 1. 9. Willingness to continue ongoing ADT. 10. Adequate organ function as defined below: * Parameter Requirement * Neutrophils ≥ 1,500/µL * Hemoglobin ≥ 12 g/dL * Platelets ≥ 100,000/µL * Creatinine ≤ 1.5 x upper limit of normal * Potassium \> 3.5 mmol/L and \<5.0 mmol/L * Total Bilirubin ≤ ULN (unless Gilbert's disease) * AST (TGO) ≤ 2.5 x ULN * ALT (TGP) ≤ 2.5 x ULN 11. 68Ga-PSMA-PET/CT performed during the screening phase showing metastatic (extraprosthetic and extrapelvic) disease with radiotracer uptake and: 12. SUVmax ≥20 in at least one site; 13. SUVmax \>10 in all other measurable metastatic sites. 14. Lesions with uptake at least 1.5 times greater than hepatic background will be considered measurable. Exclusion Criteria: 1. Presence of any small-cell or neuroendocrine component of prostate carcinoma. 2. Prior receipt of chemotherapy or radiopharmaceuticals in the castration-resistant setting. 3. Presence of another active malignancy requiring treatment or a cancer diagnosis within the past 5 years. Carcinoma in situ of any site, squamous cell carcinoma of the skin, basal cell carcinoma of the skin, or papillary bladder tumors will be allowed if previously treated. 4. Severe urinary incontinence at the investigator's discretion. 5. 18F-FDG-PET/CT will be performed during screening and will be considered exclusionary if there is discordance with the 68Ga-PSMA-PET/CT. Discordance is defined as FDG-hypermetabolic lesions with absent or low PSMA uptake (SUVmax \<10) in more than 50% of measurable metastatic lesions. 6. Patients with brain metastases visible on 68Ga-PSMA-PET/CT.