What happens if more than one pollen grain enters a stigma?

[porphyro]

Has the stigma already "closed up" after the first grain? Do the grains produce different fruits?
Perhaps the ovary as usual bears fruit, but the fruits contain more seeds?
Could it be that after the initial pollination, the stigma is infertile and so any new grains simply go to waste, like a burglar coming upon an empty shop where all the goods have already been stolen?
I have been asking this question to my tutors, colleagues, several professional botanists and many gardeners, as well as more than once on y/answers and horticultural websites, and nobody knows!

[gen2]

The stigma is just the plant equivalent of a vagina. It provides access to the female gametes. It does not close or block access whilst receptive. All pollen grains that land on a receptive stigma will grow a pollen tube down the style and into the ovary and seek out a micropyle of an ovule. Depending on the plant, the ovary may contain one or more ovules. The pollen nucleus will then pass down the tube to join with the nucleus of one of the ovules. From that pont, the ovule will not be receptive to further pollen tubules, but the stigma/style will still allow access to other ovules.

Yes, there is some feedback mechanism, because once the ovules are fertilised, the stigma dries and withers. This would happen anyway even if the plant was not fertilised but I believe it would remain receptive for longer.

I know there is more to it than that because many plants are not self-fertile so inappropriate pollen is inhibited from developing pollen tubes (plant auxins? enzymes?)

Unfortunately, I did zoology rather than botany at Uni. so that is the best I can offer.