A new systematic approach extending the notion of frames to the Palatini scalar–tensor theories of gravity in various dimensions $$n>2$$ $n>2$ is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal transformations. We characterize theories invariant with respect to these transformations dividing them up into solution-equivalent subclasses (group orbits). To this end, invariant characteristics have been introduced. The formalism provides new frames incorporating non-metricity that lead to re-definition of Jordan frames. The case of Palatini F(R)-gravity is considered in more detail.