Recently, the near-extremal geometries of Einstein Maxwell Dilaton theories have been studied as holographic quantum critical points which lie in the same universality class as the low-temperature, 'strange metallic' phase of e.g. high critical temperature superconductors. They typically display (non-)relativistic scale invariance and hyperscaling violation. We shall present a classification of these backgrounds based on their scaling properties, and then interpret it in terms of generalised dimensional reduction. Then, we shall use this same tool to show how they behave under the inclusion of specific higher-derivative operators (corresponding to departures from strong coupling), and, remarkably show that their scaling properties are preserved.