For Business-To-Business (B2Bi) scenarios, the application of choreography and orchestration technology has become a core technique for resolving discrepancies between the interaction logic of individual partners and the intended overall message flow. While orchestrations govern the message exchanges of each single partner, choreographies define constraints and requirements for the message flow between all partners. Using choreographies, B2Bi scenarios can be analyzed from a global perspective before the business services of the integration partners for implementing orchestrations are developed. So far, B2Bi choreographies mostly have been binary, i.e., performed by exactly two partners. This paper shows how multi-party B2Bi choreographies can be composed from binary choreographies, how the multi-party perspective lends itself to attacking the so-called partial termination problem and how projections for the individual partners can be derived.