Points for accumulation in nanoscale topography (PAINT) allows the acquisition of practically unlimited measurements in localisation microscopy. However, PAINT is inherently limited by unwanted background fluorescence at high probe concentrations, especially in large depth-of-field volumetric imaging techniques. Here we present reservoir-PAINT (resPAINT), in which we combine PAINT with active control of probe photophysics. In resPAINT, a "reservoir" of non-fluorescent activatable probes accumulate on the target, which makes it possible to drastically improve the localisation rate (by up to 50-fold) compared to conventional PAINT, without any compromise in contrast. By combining resPAINT with large depth-of-field microscopy, we demonstrate volumetric super-resolution imaging of entire cell surfaces. We then generalise the approach by implementing multiple switching strategies, including photoactivation and spontaneous blinking. We also implement alternative volumetric imaging modalities including the double-helix point-spread function, the tetrapod point-spread function and single-molecule light field microscopy. Finally, we show that resPAINT can be used with a Fab to image membrane proteins, effectively extending the operating regime of conventional PAINT to encompass a larger range of biological interactions.