  In this work we study diffeomorphism-invariant metric-affine theories of
gravity from the point of view of self-interacting field theories on top of
Minkowski spacetime (or other background). We revise how standard metric
theories couple to their own energy-momentum tensor, and discuss the
generalization of these ideas when torsion and nonmetricity are also present.
We review the computation of the corresponding currents through the Hilbert and
canonical (Noether) prescriptions, emphasizing the potential ambiguities
arising from both. We also provide the extension of this consistent
self-coupling procedure to the vielbein formalism, so that fermions can be
included in the matter sector. In addition, we clarify some subtle issues
regarding previous discussions on the self-coupling problem for metric
theories, both General Relativity and its higher derivative generalizations. We
also suggest a connection between Lovelock theorem and the ambiguities in the
bootstrapping procedure arising from those in the definition of conserved
currents.
