Splitting epis by wishful thinking

On Mathoverflow there is a discussion (see http://mathoverflow.net/questions/117921/relative-consistency-of-etcs-over-t...) which got me thinking. Is there a construction which "freely" splits all epis in a category C? Something like: we add sections to every epi and wish we are done? The question is somewhat lose, but I think it is clear nontheless. With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]