Most any kind of onion is very tough and can be divided and replanted most any time of year without killing them, but the exact best time to do that may vary according to type. There is more than one type of onion called multiplier ~
Bunching onions ~ Allium fistulosum ~ Welsh onions, and those green onions you buy in buches at the store
Link One, Link Two, Link Three.
Potato onions ~ Allium cepa var. aggregatum ~ shallots
Link One, Link Two, Link Three (look under "Features" near the end for a bit about potato onions, shallots, and walking/topsetting onions).
and, less often, Topsetting onions ~ Allium cepa var. proliferum ~ Egyptian walking onions, tree onions
Link One, Link Two.
And there are still more kinds of onions as well. Bulbing onions and chives come to mind.