In this paper, we extend the Support Based Distributed Optimization (SBDO) algorithm to support problems which do not have a total pre-order over the set of solutions. This is the case in common real life problems that have multiple objective functions. In particular, decision support problems. These disparate objectives are not well supported by existing Distributed Constraint Optimization Problem (DCOP) techniques, which assume a single cost or utility function. As a result, existing Distributed COP techniques (with some recent exceptions) require that all agents subscribe to a common objective function and are therefore unsuitable for settings where agents have distinct, competing objectives. This makes existing constraint optimization technologies unsuitable for many decision support roles, where the decision maker wishes to observe the different trade-offs before making a decision.