  We perform a study of possible instabilities of the infrared AdS2 x R2 region
of solutions to Einstein-Maxwell-dilaton systems which exhibit an intermediate
regime of hyperscaling violation and Lifshitz scaling. Focusing on solutions
that are magnetically charged, we probe the response of the system to spatially
modulated fluctuations, and identify regions of parameter space in which the
infrared AdS2 geometry is unstable to perturbations. The conditions for the
existence of instabilities translate to restrictions on the structure of the
gauge kinetic function and scalar potential. In turn, these can lead to
restrictions on the dynamical critical exponent z and on the amount of
hyperscaling violation theta. Our analysis thus provides further evidence for
the notion that the true ground state of `scaling' solutions with hyperscaling
violation may be spatially modulated phases.
