Inclusion dependencies form one of the most widely used classes of database dependencies. We expand existing results on the axiomatization and computational complexity of their implication problem to two extended variants. First, we present an alternative completeness proof for standard inclusion dependencies and generalize it to inclusion dependencies with repetitions that can express equalities between attributes. The proof uses only two values, enabling us to work within the Boolean setting. Furthermore, we study inclusion dependencies with Boolean constants, provide a complete axiomatization, and show that no such axiomatization is k-ary. We also establish that the decision problems for both extended versions remain PSPACE-complete. The extended inclusion dependencies are common in team semantics, which serves as the formal framework for the results.