LuX: Xaluritamig in Participants With Metastatic Castrate Resistant Prostate Cancer and Suboptimal Response to Lutetium 177 Vipivotide Tetraxetan

Primary Objective and Endpoints To evaluate the efficacy of xaluritamig following lutetium 177 vipivotide tetraxetan in patients with mCRPC, using a composite endpoint defined as the proportion of participants who achieve either of the following: * Partial or complete response up to 24 weeks by local investigator's assessment per RECIST v1.1 in participants with baseline measurable disease, with confirmation at least 4 weeks after the initial observation; OR * PSA90, defined as a decline of ≥ 90% from baseline PSA (for participants with a baseline PSA ≥ 2.0 ng/mL) up to 24 weeks, confirmed by a subsequent PSA value obtained ≥3 weeks later. Secondary Objectives and Endpoints To evaluate the safety and efficacy of xaluritamig following lutetium 177 vipivotide tetraxetan in patients with mCRPC as measured by: * Radiographic PFS * Duration of response, per RECIST v1.1 * Time to PSA response (30%, 50%, 70%, and 90%) * Time to PSA progression * Changes in laboratory safety evaluations (complete blood count \[CBC\], comprehensive metabolic panel \[CMP\], lactate dehydrogenase \[LDH\]) * Treatment-emergent adverse events (TEAE) following treatment initiation. * Duration of PSA 50/90 response Correlative/Exploratory/Tertiary Objectives The following tertiary objectives are included in this protocol for exploratory purposes. However, it is important to note that these objectives may not be pursued depending on resource availability, feasibility, or other considerations during the course of the trial. * To perform quantitative analysis of peripheral immune profile and cytokine profiles. * To perform somatic genomic analysis and measure circulating tumor cells. * To conduct immune and molecular analyses and exploratory prostate cancer biomarker studies to associate with clinical outcomes.