  We study the presence of universal bounds on transport in homogeneous
holographic models with broken translations. We verify numerically that, in
holographic systems with momentum dissipation, the viscosity to entropy bound
might be violated but the shear diffusion constant remains bounded by below.
This confirms the idea that $\eta/s$ loses its privileged role in
non-relativistic systems and that, in order to find more universal bounds, one
should rather look at diffusion constants. We strengthen this idea by showing
that, in presence of spontaneously broken translations, the Goldstone diffusion
constant satisfies a universal lower bound in terms of the Planckian relaxation
time and the butterfly velocity. Additionally, all the diffusive processes in
the model satisfy an upper bound, imposed by causality, which is given in terms
of the thermalization time -- the imaginary part of the first non-hydrodynamic
mode in the spectrum -- and the speed of longitudinal sound. Finally, we
discuss the existence of a bound on the speed of sound in holographic conformal
solids and we show that the conformal value acts as a lower (and not upper)
bound on the speed of longitudinal phonons. Nevertheless, we show that the
stiffness $\partial p/\partial \epsilon$ is still bounded by above by its
conformal value. This suggests that the bounds conjectured in the past have to
be considered on the stiffness of the system, related to its equation of state,
and not on the propagation speed of sound.
