(1) There is at most one half of an apple in the fruit bowl
sounds fine, but
(2) There is at most one half of an object in the fruit bowl
sounds odd. (I trust that others will think the same, but feel free to correct me if I’m wrong!) Surely, if an apple is an object, half an apple is half an object? But if (1) makes sense and (2) doesn’t, does that mean a half of an apple is not half an object? Perhaps the thought which drives the sense of oddness is that nothing is a half simpliciter, it is always a half of some sort of thing: One mile is half of two miles, and if we dropped the term "mile" and started calling two mile intervals “stretches”, one mile could simply be called “half a stretch”. Yet this “halfness” is nothing ontically basic; one and the same thing is half a stretch, one mile, two half-miles, and five thousand two hundred and eighty feet.
Even so, why couldn’t we have at most half of an object in the fruit bowl if “object” picks out a genuine category? If we can eat half an apple and drive half a mile, what prevents us from throwing half an object across the room? We could certainly throw half a football. The answer to these queries might be that a given entity which is a fraction of one thing is always a whole (and thus one) of something else. E.g., one slice of a pizza is also one eighth of the whole pie. We can also note that if there is at most half of an object in the fruit bowl, it cannot be the case that there is at least one, and if the bowl is not empty that is impossible. Thus we cannot say there is at most half an object in the fruit bowl; wherever we have a fraction of one sort of object there is always at least one of different sort. All this goes to show that "object" picks out a very special category if it picks out any at all.
The above reflections seem to commit us to a Fregean view in which nothing is intrinsically one or many. This view is not without its problems: Does it make good metaphysical sense to hold that how many things there are depends on what category we apply to them? Aren’t we contradicting ourselves if we say that one thing can be identical to many? After all, one deck of cards cannot be identical to two decks, why should it be any more possible for it to be identical to fifty two cards? Yet if we do not embrace the Fregean view, how else might we explain (or explain away) the strangeness of (2)? These are difficult issues, but hopefully with your input we can get a clearer view of the matter.
 “Object” being construed broadly as covering anything that exists.