A picture of what you are doing would be very helpful - hold the side of what? CA may not be the bet choice here and more does not always equal better with this adhesive.
What Martin sez...
The Korber fire escapes are actually made by Tichy Products, I do believe. They're styrene plastic. Ergo, when I've assembled these (e.g., check out the Ameritowne Midtown Hotel!!) I've used Testors Liquid Cement for styrene....the stuff in a plastic bottle with a metal needle applicator for precise, minimal application. No problem with the puddytats....or Golden Retrievers, in my case.
This cement will take care of the assembly of the fire escapes. However, if you intend to cement the F/E assembly to the Korber building, I'd recommend doing that with CA. And, yes, as Martin sez, 'More is not better'.
OTOH, because the F/E's are relatively fragile and not very forgiving should the building be moved occasionally with careless maneuvers so characteristic of homo sapiens, I've taken to adding a couple rods beneath each F/E floor which simply insert into holes bored into the building walls. That way I can deal with the F/E's (move, store, paint, etc.) separately from the building. But, TEHO......it works to my advantage, but maybe not the choice of others.
FWIW, of course......always.
KD