Cross-organizational processes naturally involve multiple stakeholders with distinct business interests. Yet, current process modeling approaches are conceptually centralized. This paper develops Colaba, a novel approach for the design of a cross-organizational process. Colaba naturally accommodates the requirements of multiple stakeholders. It is realized as a tool and methodology that uses and maintains a repository of business protocols, each describing a business function to the desired level of nuance. Design in Colaba is thus simply a matter of selecting, refining, extending, and composing protocols. Colaba is based on the concepts of Issue-Based Information Systems. It naturally supports stakeholders proposing process models, raising issues about them, and evaluating alternative proposals. Colaba contributes argumentation primitives and a representation relevant to business processes that accommodates the diverse perspectives of the roles in a protocol. This paper includes an evaluation of Colaba via a case study.