A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions 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. Unlike in the metric case, it turns out that the dimension four admitting the largest transformation group is rather special for such theories. The formalism provides new frames that incorporate non-metricity. The case of Palatini F(R)-gravity is considered in more detail.
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