Multispectral imaging is an established method to extend the number of colours usable in fluorescence imaging beyond the typical limit of three or four. However, standard approaches are poorly suited to live-cell imaging owing to the need to separate light into many spectral channels, and unmixing algorithms struggle with low signal-to-noise ratio data. Here we introduce an approach for multispectral imaging in live cells that comprises an iterative spectral unmixing algorithm and eight-channel camera-based image-acquisition hardware. This enables the accurate unmixing of low signal-to-noise ratio datasets captured at video rates, while maintaining diffraction-limited spatial resolution. We use this approach on a commercial spinning-disk confocal microscope and a home-built oblique-plane light-sheet microscope to image one to seven spectrally distinct fluorophore species simultaneously, using both fluorescent protein fusions and small-molecule dyes. We further develop protein-binding proteins (minibinders), labelled with organic fluorophores, and use these in combination with our multispectral imaging approach to study the endosomal trafficking of cell-surface receptors at endogenous levels.