Service-based business processes are often developed and deployed by single organizations. In distributed, shared resource environments like the cloud on the other hand, consumers share resources owned by cloud providers. %Higher levels of resource sharing gives more economy of scale for providers in the software-as-a-service (SaaS) or business process-as-a-service (BPaaS) space. This requires multi-tenancy capability for service processes that provides customized behaviour for on shared process implementations to meet the varying needs of different process consumers as tenants of the process resource. In this paper, we define a distributed multi-tenant architecture for BPEL processes provided as a service. A single-version BPEL process is deployed by a provider and offered for all process consumers, combined with a customization and management functionality to create a unique experience for different consumers (process tenants). We provide two core components: a policy model for consumers to express customization/business requirements of service processes and a coordination framework for policy enforcement between consumers and providers to achieve on-the-fly customization of service processes.