This paper addresses the problem of non-disjoint decomposition of multiple-valued functions. First, we show that the problem of computing non-disjoint decompositions of a multiple-valued function is related to the problem of finding multiple-vertex dominators of a logic circuit, representing the function. Second, we present an O(n^k) algorithm for computing all multiple-vertex dominators of a fixed size k, where n is the number of gates of the logic circuit. Our result is important because no polynomial-time algorithm for finding all possible non-disjoint decompositions of multiple-valued functions is known. The presented approach allows us computing a certain subset of non-disjoint decompositions (all reflected in a given circuit structure) in polynomial time. A set of experiments on benchmark circuits illustrates the efficiency of our approach.