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I have made a couple of builds that do everything, and seen several more as both a GM and as a player. These are builds that go beyond powerbuilding, and into the realm of taking over for the entire party. I'm not talking specifically about casters that do everything via magic, but rather a wider variety of builds designed to truly do everything. They cast, fight, tank, heal, and have the potential to take over entire campaigns. They have every skill, they need no party, and they don't even have the excuse of being specialized in something as generalized as "arcane casting."
Just as a few examples, I have seen an alchemist build that gets insane AC, heals, trapfinds, and has most skills in the book. On it's own, it's a monster. I have also personally created a Bard/Arcane Trickster build that gets high-level Sneak Attack, near-full Bard casting, skills for days, trapfinding, and decent physical combat potential.
As a GM, in your experience, how should I deal with players who insist on playing something that has no need for any other character in the party, in such a way that it becomes an actuality? What should I recommend that they do, other than "play a different character," so that they get to play the character they want to play and don't over-power the party?
In addition, if there are any over-powered builds/abusable mechanics in this vein that you would like to share for other GMs to be cautious of, that would be appreciated. Yes, we are aware that Wizard 20 is capable of the above in some way or another, but there are other abusable classes/builds.