Abstract: Multi-Agent Path Finding (MAPF), the problem of finding collision-free paths for multiple agents, is important in many applications, such as automated warehouses. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor $w$ of the optimal cost. \shao{On the low level, EECBS uses focal search to find bounded-suboptimal paths while reducing the number of collisions.} On the high level, EECBS uses explicit estimation search (EES) to resolve collisions. EES keeps track of a lower bound of the optimal cost ($LB$) and finds paths with sum of path costs at most $w \cdot LB$ in order to guarantee bounded suboptimality. However, many paths are typically much shorter than $w$ times their optimal path lengths, meaning that the sum of path costs is much less than $w$ times the optimal cost. In this paper, we propose Flexible EECBS (FEECBS), which uses a flex(ible) distribution of the path cost to relax the bounded-suboptimality restriction on the low level in order to further reduce the number of collisions while still guaranteeing to solve MAPF bounded-suboptimally. Flex distribution can make raising $LB$ harder, so we do not only introduce restrictions for using it but also combine it with A* search to avoid the search being slow. Our empirical evaluation shows that EECBS with flex distribution outperforms on MAPF instances with large maps and large numbers of agents and has competitive performance on MAPF instances with small maps.