Low PSMA SUV Boost (LPS-Boost): Intensified 177Lu-PSMA-617 Treatment for Patients With Metastatic Castrate-Resistant Prostate Cancer With Low PSMA Expressing Disease

Inclusion Criteria: * Patients must have the ability to understand and sign an approved informed consent. * Patients must have the ability to understand and comply with all protocol requirements. * Patients must be ≥ 18 years of age. * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. * Patients must have a life expectancy \> 6 months. * Patients must have histological, pathological, and/or cytological confirmation of prostate cancer. * Patients must have a positive 68Ga-PSMA PET/CT scan with no PSMA negative lesion, as determined by the Nuclear Medicine site investigator. The presence of PSMA-positive lesions was defined as 68Ga-PSMA-11 uptake greater than that of liver parenchyma in one or more metastatic lesions of any size in any organ system. PSMA negative disease defined as lymph nodes of 2.5 cm or visceral lesions or soft tissue component of a lytic bone lesion of 1.0 cm or larger with uptake less than that of liver parenchyma. * Patients must have whole body tumor SUVmean of \< 10 on 68Ga-PSMA PET/CT scan, as determined by the Nuclear Medicine site investigator. 68GaPSMA PET/CT will be analyzed using a semi-quantitative approach with MIM software (MIM Software Inc.). The workflow identified whole-body regions of interest (ROIs) with an maximum standardized uptake value (SUVmax) greater than 3 and a lesion size of at least 0.5 mm. The reviewer then manually removes any instances of physiological activity or uptake that are not related to the disease. The method of whole-body quantification will automatically calculate the whole body SUVmean. * Patients must have prior orchiectomy and/or ongoing androgen-deprivation therapy and a castrate level of serum testosterone (\< 50 ng/dL or \< 1.7 nmol/L) at the most recent evaluation before enrollment. * Patients must have received at least one androgen receptor pathway inhibitor (ARPI) (such as enzalutamide and/or abiraterone). * Patients must have progressive mCRPC. Documented progressive mCRPC will be based on at least 1 of the following criteria: * Serum PSA progression defined as 2 consecutive increases in PSA over a previous reference value measured at least 1 week prior. The minimal start value is 2.0 ng/mL. * Soft-tissue progression defined as an increase ≥ 20% in the sum of the diameter (SOD) (short axis for nodal lesions and long axis for non-nodal lesions) of all target lesions based on the smallest SOD since treatment started or the appearance of one or more new lesions. * Progression of bone disease: evaluable disease or new bone lesions(s) by bone scan (2+2 Prostate Cancer Working Group 3 (PCWG3) criteria, Scher et al 2016). * Patients must have ≥ 1 metastatic lesion that is present on baseline CT, MRI, or bone scan imaging obtained ≤ 45 days prior to beginning study therapy. Measurable disease by per Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 is not required, as prostate cancer patients may not have RECIST-measurable disease but have detectable disease on bone scan. * Patients must have recovered to ≤ grade 2 from all clinically significant toxicities related to prior therapies (i.e. prior chemotherapy, radiation, immunotherapy, etc.). * White blood cell (WBC) count ≥ 2.5 x 10\^9/L (2.5 x 10\^9/L is equivalent to 2.5 x 10\^3/uL and 2.5 x K/uL and 2.5 x 10\^3/cumm and 2500/uL) OR absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L (1.5 x 10\^9/L is equivalent to 1.5 x 10\^3/uL and 1.5 x K/uL and 1.5 x 10\^3/cumm and 1500/uL). * Platelets ≥ 100 x 10\^9/L (100 x 10\^9/L is equivalent to 100 x 10\^3/uL and 100 x K/uL and 100 x 10\^3/cumm and 100,000/uL). * Hemoglobin ≥ 9 g/dL (9 g/dL is equivalent to 90 g/L and 5.59 mmol/L). * Total bilirubin ≤ 1.5 x the institutional upper limit of normal (ULN). For patients with known Gilbert's syndrome ≤ 3 x ULN is permitted. * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3.0 x ULN OR ≤ 5.0 x ULN for patients with liver metastases. * Albumin \> 3.0 g/dL (3.0 g/dL is equivalent to 30 g/L). * Serum creatinine ≤ 1.5 x ULN or creatinine clearance ≥ 50 mL/min. * HIV-infected patients who are healthy and have a low risk of AIDS-related outcomes are included in this trial. HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For patients who have partners of childbearing potential: Partner and/or patient must use a method of birth control with adequate barrier protection, deemed acceptable by the principal investigator during the study and for 14 weeks after last study drug administration. The patients should not donate sperm throughout the treatment period and for 14 weeks following the last treatment. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. Exclusion Criteria: * Previous treatment with Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223 or hemi-body irradiation within 6 months prior to treatment day 1. Previous PSMA-targeted radioligand therapy is not allowed. * Any systemic anti-cancer therapy (e.g. chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\]) within 30 days prior to treatment day 1. * Concurrent bone strengthening agents such as bisphosphonates (such as zolendronic acid) and RANKL inhibitors (such as denosumab) are allowed. * Any investigational agents within 30 days prior to treatment day 1. * Known hypersensitivity to the components of the study therapy or its analogs. * Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy. * Transfusion within 30 days of treatment day 1. * Patients with a history of central nervous system (CNS) metastases must have received therapy (surgery, radiotherapy, gamma knife) and be neurologically stable, asymptomatic, and not receiving corticosteroids for the purposes of maintaining neurologic integrity. Patients with epidural disease, canal disease and prior cord involvement are eligible if those areas have been treated, are stable, and not neurologically impaired. * Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression. * Concurrent serious (as determined by the Principal Investigator) medical conditions, including, but not limited to, New York Heart Association class III or IV congestive heart failure, history of congenital prolonged QT syndrome, uncontrolled infection, active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the investigator would impair study participation or cooperation.