Nataf's theorem on consistent aggregation of micro-relationships - reqUiring separability - is reconsidered with a view to: (a) streamlining the derivation of the theorem beyond the stage carried through by Green; (b) relaxing some of the conditions formerly required for that purpose, in particular the differentiability of the functions; (c) generalizing the originally "single-output", two-dimensional aggregation theorem to multiple outputs and to three (and more) dimensions.