Fluorescence microscopy is rapidly turning into nanoscopy. Among the various nanoscopy methods, the STED/RESOLFT super-resolution family has recently been expanded to image even large fields of view within a few seconds. This advance relies on using light patterns featuring substantial arrays of intensity minima for discerning features by switching their fluorophores between 'on' and 'off' states of fluorescence. Here we show that splitting the light with a grating and recombining it in the focal plane of the objective lens renders arrays of minima with wavelength-independent periodicity. This colour-independent creation of periodic patterns facilitates coaligned on- and off-switching and readout with combinations chosen from a range of wavelengths. Applying up to three such periodic patterns on the switchable fluorescent proteins Dreiklang and rsCherryRev1.4, we demonstrate highly parallelized, multicolour RESOLFT nanoscopy in living cells for ~100 × 100 μm(2) fields of view. Individual keratin filaments were rendered at a FWHM of ~60-80 nm, with effective resolution for the filaments of ~80-100 nm. We discuss the impact of novel image reconstruction algorithms featuring background elimination by spatial bandpass filtering, as well as strategies that incorporate complete image formation models.