Stabilized explicit implicit domain decomposition (SEIDD) is a class of globally non-iterative domain decomposition methods for the numerical simulation of unsteady diffusion processes on parallel computers. By adding a communication-cost-free stabilization step to the explicit-implicit domain decomposition (EIDD) methods, the SEIDD methods achieve high stability but with the restriction that the interface boundaries have no crossing-overs inside the domain. In this paper, we present a parallelized SEIDD algorithm with paralellism higher than the number of subdomains, eliminating the disadvantage of non-crossing-over interface boundaries at a slight computation cost.