  The Eigenstate Thermalization Hypothesis (ETH) has played a key role in
recent advances in the high energy and condensed matter communities. It
explains how an isolated quantum system in a far-from-equilibrium initial state
can evolve to a state that is indistinguishable from thermal equilibrium, with
observables relaxing to almost time-independent results that can be described
using traditional statistical mechanics ensembles. In this work we probe the
limits of ETH, pushing it outside its prototypical applications in several
directions. We design a qutrit lattice system with conserved quasilocal charge,
in which we verify a form of generalized eigenstate thermalization. We also
observe signatures of thermalization in states well outside microcanonical
windows of both charge and energy, which we dub `generic ETH.'
