  We consider the stability of self-accelerating solutions to extended
quasidilaton massive gravity in the presence of matter. By making a second or
extended fiducial metric dynamical in this model, matter can cause it to evolve
from a Lorentzian to Euclidean signature, triggering a ghost instability. We
study this possibility with scalar field matter as it can model a wide range of
cosmological expansion histories. For the $\Lambda$CDM expansion history,
stability considerations substantially limit the available parameter space
while for a kinetic energy dominated expansion, no choice of quasidilaton
parameters is stable. More generally these results show that there is no
mechanism intrinsic to the theory to forbid such pathologies from developing
from stable initial conditions and that stability can only be guaranteed for
particular choices for the matter configuration.
