Over the past 18 months we have revisited the science requirements for a multi-object spectrograph (MOS) for the European Extremely Large Telescope (E-ELT). These efforts span the full range of E-ELT science and include input from a broad cross-section of astronomers across the ESO partner countries. In this contribution we summarise the key cases relating to studies of high-redshift galaxies, galaxy evolution, and stellar populations, with a more expansive presentation of a new case relating to detection of exoplanets in stellar clusters. A general requirement is the need for two observational modes to best exploit the large (>= 40 arcmin(2)) patrol field of the E-ELT. The first mode ('high multiplex') requires integrated-light (or coarsely resolved) optical/near-IR spectroscopy of >100 objects simultaneously. The second ('high definition'), enabled by wide-field adaptive optics, requires spatially-resolved, near-IR of >10 objects/sub-fields. Within the context of the conceptual study for an ELT-MOS called MOSAIC, we summarise the top-level requirements from each case and introduce the next steps in the design process.