1- synthesis should be done with the worst corner(s) to reach the setup constraints.
2- place & route, I usefully have in MMMC flow, how many setup condition, where I want to be sure my design must reach the setup constraints, and for the hold condition, all corners I want to have my design to be functional. I mean, some corners do not have a specific setup condition, but I want to be sure the chip works properly.
3- STA, I checks setup & hold, in all corners used before with the three RC extractions.