The exact composition of mechanisms for which two differential privacy (DP) constraints hold simultaneously is studied. The resulting privacy region admits an exact representation as a mixture over compositions of mechanisms of heterogeneous DP guarantees, yielding a framework that naturally generalizes to the composition of mechanisms for which any number of DP constraints hold. This result is shown through a structural lemma for mixtures of binary hypothesis tests. Lastly, the developed methodology is applied to approximate f-DP composition.