We introduce a family of information leakage measures called maximal $α,β$-leakage, parameterized by real numbers $α$ and $β$. The measure is formalized via an operational definition involving an adversary guessing an unknown function of the data given the released data. We obtain a simple, computable expression for the measure and show that it satisfies several basic properties such as monotonicity in $β$ for a fixed $α$, non-negativity, data processing inequalities, and additivity over independent releases. Finally, we highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal $α$-leakage $(β=1)$, maximal leakage $(α=\infty,β=1)$, local differential privacy $(α=\infty,β=\infty)$, and local Renyi differential privacy $(α=β)$.