Tensor splitting iteration method is a class of popular technique for solving multi-linear systems. In this paper, we present one kind of efficient alternating splitting iteration method, and further generalize accelerated overrelaxation method (AOR) and symmetric accelerated overrelaxation method (SAOR) from linear systems to multi-systems. Then, one type of preconditioned (alternating) tensor splitting method is also applied for solving multi-systems. Numerical experiments illustrate the efficiency of the provided methods.