The goal of this study was the development and evaluation of an algorithm for resolving conflicting requests for transit signal priority (TSP). This algorithm was designed to work with actual traffic controllers without the need for new hardware or software installations. The algorithm was tested in VISSIM microsimulation and ASC/3 software-in-the-loop controllers on an intersection that will be upgraded to serve two conflicting bus rapid transit (BRT) lines. The ASC/3 logic processor was used to control built-in TSPs in the case of conflicting requests and to develop custom-TSP strategies that would not rely on built-in TSP. Custom TSP provides a much higher level of TSP for transit vehicles than built-in TSP, and it creates opportunities for more adaptable TSP control. The results showed that the widely used first-come, first-served policy for resolution of conflicting TSP requests was not the best solution. Such a policy could perform worse than a policy that provided no priority. For the analyzed intersection, the first-come, first-served option even increased BRT delays by 13% more than did the no-TSP option. The presented algorithm can help resolve the problem of the conflicting TSP requests. The algorithm worked best when combined with several TSP strategies. For the custom-TSP strategies, the application of the algorithm reduced BRT delays by more than 30%, with minimal impact on vehicular traffic. The algorithm shows promising results, and with small upgrades, it can be applied to any type of TSP.