Sockets are often handy, I haven't squashed on yet doing such things with them, but I'm sure it's possible if one doesn't think. Best I can tell good safety (I.E. a lack of explosive disassembly events) and results on a press is all in a well thought out setup.
If the press is flat on top put a piece of plywood or whatever on top to act as a shelf to hold tooling.
Keep large bearing races and whatnot, I've often pushed in a new bearing that had to go below flush using an old one lightly ground on the OD to slip into the bore, and then on the shelf it goes.
Cardboard box underneath with some extra cardboard or rags in the bottom is also handy so you don't have to catch things as they're pressed free or worry about them getting dinged up hitting the floor (or vice versa).