/ AbstractWide-field multi-object spectroscopy is a high priority for European astronomy over the next decade. Most 8-10m telescopes have a small field of view, making 4-m class telescopes a particularly attractive option for wide-field instruments. We present a science case and design drivers for a wide-field multi-object spectrograph (MOS) with integral field units for the 4.2-m William Herschel Telescope (WHT) on La Palma. The instrument intends to take advantage of a future prime-focus corrector and atmospheric-dispersion corrector that will deliver a field of view 2 deg in diameter, with good throughput from 370 to 1,000 nm. The science programs cluster into three groups needing three different resolving powers R: (1) high-precision radial-velocities for Gaia-related Milky Way dynamics, cosmological redshift surveys, and galaxy evolution studies (R = 5,000), (2) galaxy disk velocity dispersions (R = 10,000) and (3) high-precision stellar element abundances for Milky Way archaeology (R = 20,000). The multiplex requirements of the different science cases range from a few hundred to a few thousand, and a range of fibre-positioner technologies are considered. Several options for the spectrograph are discussed, building in part on published design studies for E-ELT spectrographs. Indeed, a WHT MOS will not only efficiently deliver data for exploitation of important imaging surveys planned for the coming decade, but will also serve as a test-bed to optimize the design of MOS instruments for the future E-ELT.