  We generalize the algorithm that establishes the correspondence between
metric-affine Eddington-inspired Born-Infeld (EiBI) gravity and General
Relativity (GR) to any bosonic matter sector. Along the way, a polished version
of the proof of existence of a metric compatible frame associated to any
metric-affine Ricci-Based Gravity (RBG) is presented. Particular attention is
given to the problem of generating solutions of a RBG from the GR conterpart,
providing a general recipe for the EiBI case. This extends previous results
obtained for specific matter that included anisotropic fluids, scalar fields
and electromagnetic fields.
