  In the context of holography applied to condensed matter physics, we study
Einstein-Maxwell-dilaton theory with curvature squared corrections. This theory
has three couplings eta_i for the three R^2 invariants and two theory
functions: a dilaton potential V(phi) and a dilaton-dependent gauge coupling
f(phi). We find hyperscaling violating solutions of this theory, parametrized
by dynamical critical exponent z and HSV parameter theta. We obtain
restrictions on the form of the theory functions required to support HSV-type
solutions using three physical inputs: the null energy condition, causality z
$\leq$ 1, and d_eff = d - theta lying in the range 0 < d_eff $\leq$ d. The NEC
constraints are linear in the eta_i and (quartic) polynomial in d,z,theta. The
allowed ranges of z,theta change depending on the signs of eta_i. For the case
of Einstein-Weyl gravity, we further narrow down the theory functions and
solution parameters required for crossover solutions interpolating between HSV,
AdS_d+2 near the boundary, and AdS_2 x R^d in the deep interior.
