Dung's Abstract Argumentation Framework has been generalized in various directions. We combine two of these generalizations: Bipolar Argumentation Frameworks (BAFs), where a relation representing supports between arguments is added, and Incomplete Argumentation Frameworks (IAFs), where the existence of arguments and attacks may be uncertain. We discuss how the notion of completion of IAFs can be adapted to take into account the nature of the support relation, providing a couple of alternative definitions. After that, we analyse the impact of choosing among these alternatives on the complexity of argument acceptability problems. Finally, we give a logical encoding of our new framework in the Dynamic Logic of Propositional Assignments.