Multiple constant multiplication (MCM) algorithms are often used in hardware implementations to reduce the power, area, and latency of multiplications with constants. The most common application is the construction of FIR filters. In this paper, we introduce two improvements for a specific category of MCM algorithms, common subexpression elimination (CSE). The first is the generalized search for overlapping digit patterns (ODPs), which can find patterns of any weight. The second is the priority based selection of common subexpressions, specifically when there is a tie in maximum weight. After applying these modifications to Lefevre’s algorithm, we saw the adder cost improve by up to 3.18%. Furthermore, this resulted in no impact to the time complexity of the original algorithm.