Compressed pattern matching is one of the most active topics in string matching. The goal is to find all occurrences of a pattern in a compressed text without decompression. Various algorithms have been proposed depending on underlying compression methods in the last decade. Although some algorithms for multi pattern searching on compressed text were also presented very recently, all of them are only for Lempel-Ziv family compressions. In this paper we propose two types of multi pattern matching algorithms on collage system, which simulate the AC algorithm and a multi pattern version of the BM algorithm, the most important algorithms for searching in uncompressed files. Collage system is a formal framework which is suitable to capture the essence of compressed pattern matching according to various dictionary based compressions. That is, we provide the model of multi pattern matching algorithm for any compression method covered by the framework.