  We show how to decoupling two spherically symmetric and static gravitational
sources through the most general possible extension of the so-called Minimal
Geometric Deformation-decoupling. As a test, we decouple the Einstein-Maxwell
system and reproduce the Reissner-Nordstrom black hole solution. We show the
potential of this method to study i) the consequences of modified gravity on
general relativity, ii) to investigate the conjectured dark matter, and iii) to
study hairy black holes.
