Compression via Substring Enumeration (CSE) is a lossless universal data compression scheme, introduced by Dube and Beaudoin . CSE compresses a target binary string by enumerating substrings occurred in it, and encodes the numbers of occurrences effectively, by calculating its upper-bound and lower-bound based on the previous numbers. They used a data structure called Compacted Substring Tree (CST) for counting the occurrences. Instead of CST, Kanai et al.  proposed an elegant and efficient implementation for CSE by utilizing Burrows-Wheeler Transform (BWT) Matrix and several auxiliary arrays. In this paper, we extend it in two ways, (1) to deal with the explicit phase awareness for byte-oriented source, and (2) to treat multiple characters for a finite alphabet source.