Inclusion Criteria:  Male, aged 18 years or older Pathologically confirmed adenocarcinoma of prostate or a clinical presentation consistent with prostate cancer Metastatic castrate resistant prostate cancer previously confirmed on 68Ga-PSMA-11 and 18F-FDG imaging to be inadequate for future PSMA-directed theranostic treatment by a nuclear medicine physician based on FDG-discordance (FDG-positive, PSMA-negative sites of disease) OR low PSMA SUV values within 2 weeks of starting study drug Adequate hematologic and organ function within 14 days before the first study treatment Castrate levels of testosterone < 1.7 ng/ml Provision of written informed consent.  Exclusion Criteria:  Patients who cannot lie still for at least 30 minutes or comply with imaging. Previous dasatinib for prostate cancer or other condition, eg CLL Allergy to dasatinib or darolutamide Use of drugs that interact with interact pharmacologically with dasatinib within 1 week of study entry eg Use of CYP3A4 inducers (e.g. dexamethasone, phenytoin, carbamazepine, rifampicin, phenobarbital or St John's Wort) and use of CYP3A4 substrates with narrow therapeutic index (e.g. astemizole, terfenadine, cisapride, pimozide, quinidine, bepridil or ergot analogues. Use Concomitant use of H2 antagonists or proton pump inhibitors. Current or previous (within the last 6 months) pleural effusion Use of paracetamol during the study period Subjects may not have any of the following: Clinical evidence of uncontrolled heart failure, myocardial infarction, or angina within the previous 6 months; prolonged QT interval Fridericia's (QTcF) > 450msec; history of unstable ventricular arrhythmias (ventricular tachycardia, ventricular fibrillation, or torsades de pointes); concomitant use of drugs known to cause torsades de pointes [quinidine, procainamide, disopyramide, amiodarone, sotalol, ibutilide, dofetilide, erythromycins, clarithromycin, chlorpromazine, haloperidol, mesoridazine,thioridazine, pimozide, cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone, halofantrine, levomethadyl,pentamidine, sparfloxacin, lidoflazine] (these agents must have been discontinued at least 7 days prior to starting dasatinib) Subjects may not be enrolled with any of the following: History of a significant bleeding disorder unrelated to cancer, including diagnosed congenital bleeding disorders (e.g., von Willebrand's disease), and diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies); GI bleeding from any cause within 3 months