When playing 4 player in person, the one suggestion I would make is to not go with a fully random kingdom. Randomly generate, but then tweak. (e.g.If you don't want a slog, don't play Mountebank.) When playing multiple games, swap out a couple cards rather than re-randomizing completely every game. Go with kingdoms that appear weak-ish, rather than where all 10 kingdom cards feed into this super-engine you would like to play in 2P. Consider including some kind of alt VP.
On strategy:
Stick with simple decks. Note, not necessarily just big money (even though big money is usually better), just avoid big engine that rely on playing tons of cards every turn to get anywhere. They are viable less often than in 2P. If your proposed engine requires you grabbing half or more of 3 or 4 stacks, then you are very likely going to be beat by another player if more than one of you goes for the engine. Engines that rely on really thin decks (not a lot of cards) with lots of trashing are still viable. Or decks that are more bloated but aim to play a couple key cards a turn are okay, too.
Engine decks that require a lot of cards are hurt because you cannot control the endgame like in 2P. In my play group, if one of us undertakes a dubious long-game engine, the other 3 players will start attacking piles after figuring out what's coming. Even if you've found "the deck", you are still racing, and the other players can more easily correct their play than in 2P.
You have to pull the trigger on the engine earlier than you would in 2P, so engines that require "overbuilding" are just not going to work. Need 6 or 7 bridges to empty VP piles in one turn? Don't count on getting them. Your deck better be able to do something if you only get 3, instead.
Slogs are more likely because of the stackable nature of a lot of attacks. (Mountebank means slog. Almost always.) Alt VP is usually more viable as an actual alternative strategy. The alt vp dynamics are usually more interesting, too.
"Bad" cards become much better (Except Scout. It's still bad), especially the treasure attacks, and you often get a chance to build decks you otherwise wouldn't in 2P. There are great 4p games I've played with Pirate Ship, Noble Brigand, Thief, etc. Playing with 3-5 players really shows that the weak treasure and treasure attack cards are much more balanced for those games even though they are usually pretty bad in 2P.
Really, really watch out for piles.
I also rarely count except on a very superficial level because there is much less you can do to control the end of the game.
