Canonical quotients

Peter Freyd's and John Kennison's examples definitively settled Mike Barr's question about canonical subobjects that compose. But I had started thinking about it and had what I thought would be a nice example. The category of sets has canonical quotients (equivalence classes) but they don't compose. I think there is no choice that do, but so far I haven't been able to prove or disprove this. Anybody? Bob [For admin and other information see: http://www.mta.ca/~cat-dist/ ]