The fields of view of Extremely Large Telescopes will contain vast numbers of spatial sampling elements (spaxels) as their Adaptive Optics systems approach the diffraction limit over wide fields. Since this will exceed the detection capabilities of any realistic instrument, the field must be dilutely sampled to extract spectroscopic data from selected regions of interest. The scientific return will be maximised if the sampling pattern provides an adaptable combination of separated independent spaxels and larger contiguous sub-fields, seamlessly combining integral-field and multiple-object spectroscopy. We illustrate the utility of this Diverse Field Spectroscopy (DFS) to cosmological studies of galaxy assembly. We show how to implement DFS with an instrument concept: the Celestial Selector. This integrates highly-multiplexed monolithic fibre systems (MFS) and switching networks of the type currently available in the telecommunications industry. It avoids bulky moving parts, whose limitations were noted in Paper I. In Paper III we will investigate the optimisation of such systems by varying the input-output mapping.