Mine would have to be bananas. For each banana I plant, I seem to get five more. Now that garbage season is over (winter), they're multiplying like crazy and sending up new pups. Yes, I already have them in the ground now.

Oh wow, I have two that spent summer outside last year, one in a pot on the dirt (it let its roots out of the pot and into the ground anyway so I potted it up in the fall) and the other directly in my raised bed w/ mushroom compost. I actually bought the second one because my first one was broken in half by some animal. I figured it was a gonner and bought a new one, but it totally rebounded. I thought my newer one s was a gonner just a few weeks ago. It started to lose all its leaves and the inside (newest leaf) was black too. I cut it down to 1/3 its size and yeah all black. It decided to come back and is up a few inches w/ new growth :o)
So you have yours outside already, huh? Just keep watch of the weather channel and cover if frost is looming? I haven't had any pups yet, hoping that maybe this year. Oh wow, I rambled on a lot there, I better stop now :op

my oriental lilies multiply rapidly also.
i divide them not once, but TWICE per year, in the spring and the fall. they crowd themselves, competing for sunlight. i really decimated the ones around the mailbox last fall, leaving very little behind, thinking that nothing would reappear this year, and i'd try something different there.
but there they are, coming up all over the place.
admittedly, that's probably my fault. there are some areas that i will not mulch, using my own compost instead.

for the first time since i planted them 3 years ago, my primrose are beginning to spread out a little bit.

last year somebody gave us a HUGE hosta division which we broke into 3" diameter plugs. this year they are coming up at twice that size. more for the deer, i guess.

and of course there is monarda. wow, does that stuff spread. i've divided it and placed it in different spots and it grows no matter where i put it.

Yes, my momarda has spread...all over the neighborhood! My Ozark Sundrops are also starting to form a blanket in one spot. I just moved some lilies and hope they do as well as the rest of yours have. My weeds are doing pretty well, also.

Some daffodils icrease so quickly for me that they are invasive. Hostas are easy to divide, and I do it frequently when I want additional plants of a certain variety. With smaller leaved hostas, it is often possible to divide them when you bring them home from the nursery; look for full pots!

If you are looking to increase the number of plants that you have, you could set aside a small bed where you could plant smaller divisions and let the grow until they are large enough to fill the desired spot or to divide again.