  In the framework of a two-band model, we study the phase separation regime of
different kinds of strongly correlated charge carriers as a function of the
energy splitting between the two sets of bands. The narrow (wide) band
simulates the more localized (more delocalized) type of charge carriers. By
assuming that the internal chemical pressure on the CuO$_2$ layer due to
interlayer mismatch controls the energy splitting between the two sets of
states, the theoretical predictions are able to reproduce the regime of phase
separation at doping higher than 1/8 in the experimental pressure-doping-$T_c$
phase diagram of cuprates at large microstrain as it appears in overoxygenated
La$_2$CuO$_4$.
