  We show that maximally twisted mass fermions can be employed to regularize on
the lattice the fully unquenched QCD+QED theory with vanishing $\theta$-term.
We discuss how the critical mass of the up and down quarks can be conveniently
determined beyond the electroquenched approximation by imposing that certain
symmetries of continuum QCD+QED, which are broken by Wilson terms, get restored
in the continuum limit. A mixed action setup is outlined that allows to extend
beyond the electroquenched approximation the computation (with only O($a^2$)
artifacts) of the leading isospin breaking corrections to physical observables
using the RM123 method and (pure QCD) ETMC gauge ensembles with $N_f=2+1+1$
dynamical quark flavours.
