Community search has been extensively studied in large networks, such as Protein-Protein Interaction (PPI) networks, citation graphs, and collaboration networks. However, in terms of widely existing multi-valued networks, where each node has $d$ ( $d\mathrm{⩾}\mathrm{1}$) numerical attributes, almost all existing algorithms either completely ignore the attributes of node at all or only consider one attribute. To solve this problem, the concept of skyline community was presented, based on the concepts of $k$-core and skyline recently. The skyline community is defined as a maximal $k$-core that satisfies some influence constraints, which is very useful in depicting the communities that are not dominated by other communities in multi-valued networks. However, the algorithms proposed on skyline community search can only work in the special case that the nodes have different values on each attribute, and the computation complexity degrades exponentially as the number of attributes increases. In this work, we turn our attention to the general scenario where multiple nodes may have the same attribute value. Specifically, we first present an algorithm, called MICS, which can find all skyline communities in a multi-valued network. To improve computation efficiency, we then propose a dimension reduction based algorithm, called P-MICS, using the maximum entropy method. Our algorithm can significantly reduce the skyline community searching time, while is still able to find almost all cohesive skyline communities. Extensive experiments on real-world datasets demonstrate the efficiency and effectiveness of our algorithms.