What kind of rule changes have you folks tried at your tables, and how have they worked out for your games? Good? Bad?
Two of the houserules I implement for every campaign I run:
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No multiclassing until after 5th level, and no further multiclassing unless you have at least 5 levels in all your existing classes. I do this for two reasons, the first being to ensure that every character has access to extra attack/third level spells and slots/some other equivalent before they start dipping elsewhere, and to keep the munchkins at my table from taking multiple 1-3 level dips into classes just to set up a niche wombo combo. Even then, I'm pretty stringent on what I'll allow from a storytelling perspective - I want to know what motivates your Paladin to dip into Warlock besides getting to use CHA for attack and damage modifiers.
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Instead of an ASI or a Feat, every ASI level gives a +1 and a feat. My players and I like this rule because it allows them to pick something fun at those levels instead of feeling obligated to dump straight into the primary stat, and encourages grabbing those fun half-feats like Actor or Linguist that would otherwise go by the wayside.
I actually don't mind killing PCs with some of the above here - not saying that I seek out opportunities, but I've played with squishy casters who are bold and/or dumb enough to wade into the enemy's back line to take advantage of short range AoEs like Burning Hands and Thunderwave, and you better believe their response is to beat the ever-loving shit out of that caster so they don't get up and do it again. And past the opportunities that cocksure players give you, it is 100% okay if a character dies, even one that a player has invested in - adventuring is dangerous and combat is especially brutal; the dragon's not going to reposition themselves to exclude a downed PC from their breath attack, the vampire's not going to pass up an easy meal from an incapacitated caster. If your games are going to be impactful and climactic, the stakes need to be real, and you can't pull any punches.
But there is an important caveat in all this - what's not okay is trivializing PC deaths, whether they died through pure chance, or wildly unbalanced encounters that end in TPKs, because that (especially the latter) ruins games and creates players who invest nothing in their characters, or worse, start to see everything as a numbers game and work to build the murderhoboiest character they possibly can. If a PC dies, it needs to be a scene. After combat's over, make a point of narrating the aftermath. Give the PC last rites, have the surviving members of the party talk about their favorite moments. Some of the best, most heart-wrenching sessions I've run are the ones where a character dies.