I only have 2 platforms, in a quite well-lit-up area, and get a few stacks per real day; I use an iron golem standing on a post in the middle, and a cactus with hoppers around it; they hop toward the IG and die on the cactus.
I have that type of farm in my current SSP worlds, both with 2 diagonally adjacent slime chunks (but only 1 level).
In my older world I have done a lot of area prep, and even with a single level that farm cranks out slime.
It's hard to get into the room to empty the chest sometimes, because there are almost always slimes.
I actually did the area prep for my creeper spawner, which is attached to my iron farm and located almost directly above the slime farm, so I was quite surprised at the effect the area prep had on the slime farm. I would have thought that more creepers spawning would mean less slime, but both farms jumped in output dramatically, in spite of their close proximity.
So area prep really is important, but the OP needs to actually find some slime chunks first.