A key issue in process-aware e-commerce collaboration is to orchestrate business processes of multiple business partners throughout a supply chain network in an automated and seamless way. Since each partner has its own internal processes with different control flow structures and message interfaces, the real challenge lies in verifying the correctness of process collaboration, and reconciling conflicts in an automated manner to make collaboration successful. The purpose of business process adaptation is to mediate the communication between independent processes to overcome their mismatches and incompatibilities. The goal of this article is to develop and compare efficient approaches of optimal adapter (i.e. one that minimizes the number of messages to be adapted) creation for multiple interacting processes under both synchronous and asynchronous communication. We start with an analysis of interactions of each message pair, and show how to identify incompatible cases and their adaptation elements for both types of communication. Then, we show how to extend this analysis into more general cases involving M messages and N processes (M, N > 2). Further, we present optimal adapter creation algorithms for both scenarios based on our analysis technique. The algorithms were implemented in a Java-based prototype system, and results of two experiments are reported. We compare and discuss the insights gained about adapter creation in these two scenarios.