That depends upon what you call “small cell”. The Mann Lake PF frames are stamped with 4.9mm sized cells. There are 25.4mm per inch. So 1 linear inch of comb crosses 25.4/4.9 = 5.18 cells. 1 square inch area of comb then has 5.18 x 5.18 = 26.8 cells. The Mann Lake PF frames really have a lot more cells than normal deep frames for 2 reasons. The cells size is smaller AND there is less space consumed by the supporting plastic frame. The skinnier plastic supporting frames though seem to result in more burr comb, so it’s not a win win type of situation.
As for how many of your super jumbo 18” x 4 foot tall frames to use in a brood box; I’m going to assume your giant frames are going to need a beefier wood support than normal. So I’ll assume you end up with a comb area of about 17”x47”. That’s 799 sq inches of comb space. If by small cell, you’re talking 4.9mm, that gives you 26.8 cells per sq inch IFF the bees comb it all up as worker cells. On the big combs they’re not going to comb them all up as worker cells so you have to adjust the numbers a little bit due to bigger drone cells. You can fudge factor later.
So you have 799 sq feet x 26.8 cells per sq inch = 21469 cells per side of frame = 42939 cells per frame. The queen doesn’t lay in the outer two frames in the brood chamber (normally) so you really can’t count those cells in your calculations of queen laying ability vs available cells. I base my capacity designs on the available cells NOT counting the outer 2 frames.
So if you go with a 3 frame design, you can’t really count on your queen having any more than 42939 cells to lay in. That is not enough. If you go with a 4 frame brood nest, then your queen has 85,878 cells for potential brood. However the bees never brood the big frames up to 100% capacity. 70% would be a good estimate in my opinion. So a 4 frame hive using your super jumbo frames would have about 85,878 x 0.70 = 60114 cells for brood. The brood cycle is 21 days, so 60114 cells could satisfy a queen laying up to 2862 eggs a day. That is a LOT of descent sized eggs from a not so large queen everyday. I doubt many queens get close to that number.
Let’s assume you do have prolific queen that could fill that capacity. Two brood cycles would yield you a hive over 120,000 bees! 3 cycles and you’re up to 180,000 bees. Do you really want to deal with THAT many bees? Maybe, but certainly not more than that. :-D