Frogleg wrote:

... But I've never seen/heard of regular ol' supermarket eating onions
multiplying in the ground...



I've never tried it with one from the supermarket, but the onions I grow
for eating sometimes double during normal growth. What usually happens
is that you get two ring structures inside of one bulb, the rings being
flattened on the common side. If left to sprout, you will get two
separate sprouts. I don't recall ever seeing three or more. I don't
recommend counting on this as a way to produce more onions from a single
one, since it's sporadic. Moreover, starting with a mature onion (as
opposed to an onion set) will only encourage flowering and seeding
rather than bulb growth. I generally start my onions from seed.

Shallots started from seed produce mostly single bulbs. Shallot bulbs
planted produce mostly multiple bulbs, numbers ranging from 2 to 5.