Multi-Agent Path Finding (MAPF) is a planning problem where multiple agents on a graph are assigned a path to their respective goals without collisions. In practical applications to the problem, such as for navigation in an automated warehouse, MAPF must be solved iteratively and in real-time. In this paper, we extend a recently developed promising solver, Priority Inheritance with Backtracking (PIBT), and propose a generalization of PIBT to cope with various scenarios. We empirically demonstrate that this generalization yields effective plans compared to the original.