Multi-enterprise processes (MEPs) are workflows consisting of a set of activities that are implemented by different enterprises. Tightly coupled Virtual Enterprises (VEs) typically agree on abstract MEPs (reference MEPs), to which each enterprise contributes single-enterprise processes (SEPs) that implement and refine the activities in the reference MEP. On the other end of the spectrum, loosely coupled VEs use service-based MEPs that fuse together heterogeneous services implemented and provided by different enterprises. Existing process models usually couple activities with their implementation. Therefore, they cannot effectively support such MEPs. In this paper, we introduce a Polymorphic Process Model (PPM) that supports both reference process- and service-based MEPs. To accomplish this, PPM decouples activity interface from activity implementation, and provides process polymorphism to support their mapping. In particular, PPM determines activity types from the activity interfaces, permits activity interface subtyping, and provides for the mapping of MEP activity types to concrete implementations via interface matching. We illustrate that these key PPM capabilities permit the late binding and use of multiple activity implementations within a MEP without modifying the MEP at run time or enumerating the alternative implementation at specification time.