; receivers, etc., might not lead to contradictions and a generalization
&gt; of it might be OK in the SUO.

If the augmented axiom doesn't lead to contradictions, surely the
unaugmented one doesn't, as it is logically weaker.  You seem to be
confusing failure to assert P with asserting that P is false.  From the
fact that the unaugmented axiom does not say that there is exactly one
giver (receiver, given) in a giving event, it does not follow that it is
asserting that there there is *not* exactly one giver