  While the Bekenstein-Hawking entropy is the unique notion of entropy that
makes classical black hole thermodynamics consistent, alternative entropy
notions (R\'enyi, Tsallis, and generalized constructs) abound in the
literature. We explore conditions under which they are part of a consistent
horizon thermodynamics for certain classes of modified gravity black holes. We
provide examples in which black hole masses and temperatures going hand-in-hand
with these alternative entropies coincide with their usual counterparts
associated with the Bekenstein-Hawking entropy.
