AI-based process model analysis has attracted more and more interest. Model quality is crucial for such research. At present, inter-organizational business process (IOBP) has been widely used in the model design and development of the distributed system. Before implementing the intelligent analysis of the IOBP model, conformance as a foundation for model quality checking plays a key role because it ensures in advance that the participants can successfully interact without violating the global communication constraints imposed by the choreography. In fact, the multi-instance participant is a common requirement in IOBP. This paper provides a formal approach and framework supporting the conformance between BPMN choreography and collaboration while considering multi-instance participants and message communication modes. As a core, the formalization proposed is based on BNF syntax and structured CSP# processes. It can well support multi-instance features and multiple communication modes. Combined with CSP#, the formal definitions of communication modes and verification properties are given. On this basis, an integrated framework is provided to support automated formal verification referring to multiple communication modes. Finally, a set of experiments is conducted to demonstrate the effectiveness of the proposal.