You may leave them to grow in a clump for one more year, but eventually you have to divide them anyway, otherwise you'll end up with a zillion of unproductive offsets competing for the finite amount of available nutrients.
The same thing as with daffodils.

Will I get more bloom next year if I divide them this fall? Wait til the stalks turn yellow?

That is, if it ever stops raining. I fully expect lots of things to die from drowning.

Pixie Lilies are great for edges. I have hundreds in various colors. If you leave the clump together too long the roots of the new bulbs may choke out the origial for food. I'd seperate them now and give at least 2" for spreading depending on how close a group you want. This year I seperated a clump which had 6 "new" bulbs 3 years ago and this year it had 27. So they do quite well. It is obvious the your clump is not getting enough nutrients to each bulb by the lack of blooms. Seperate everything , check carefully some will be very small. Pixie bulbs are small enough when full size, even smaller as babies. As with ALL LILIUMS....they are very strong plants and handle abuse well. But DO NOT over water. Better too dry than too wet. Since this is 2nd year you will be very happy with Lilies the more you get the more you want. There isn't much that will kill them except too wet. You do know they need too stay in ground and be frozen? You can dig and move as soon as the leaves turn brown. All LILIUMS, pixie or otherwise can be treated the same. Do you have normal size ones? On those you can propogate by: look around the stalk right where it joins the bulb for small "new bulbs about 1/2" or less, You can pull off a few (5-6) "flakes" off each bulb to get a new plant (plant only 1/4" deep), look on the top half of the stalk for very small bulblets next to a leaf (less than 1/4"), seed pods. In my opinion Tulips are very tough but Lilies are even tougher to kill. Go for it.

Thanks for all the great info! As it happens I have more lilies on order, speciosum album, Black Beauty, and Orienpet "Honeymoon". Since I will be digging soon for these I might as well divide the pixies too. My other asiatics and orientals are yellowing now, these pixies are still pretty green. When I bought the pot of pixies they were so rootbound I couldn't even see the bulbs. I was leaving town so had to plunk the whole thing in the ground. When I dig them out this time maybe I'll soak them in a bucket until they can be teased apart. If there's a better way let me know!

Just today I saw a cluster of bulb-like things on one asiatic, right where the stem meets the ground. Are those what I can remove and plant? Can I do that without disturbing the main bulb? I had to move most of the asiatics (not the one that has the bulblets now) early this spring when I found them crowded by a very fast-growing perennial. Since they were already 6 inches high I think moving them impacted bloom. I don't want to move them if that will happen again.

Is there a general rule of thumb for how often bulbs need to be divided?