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 also like to abide by in-character reasons to multiclass, though I haven’t had any particular problem players in this regard.
In a similar spirit to your second rule, I like to start off PCs with a free feat since they can be so flavorful for both mechanics and roleplay. I’ve also given martials a maneuver of their choosing to give martials more to do in combat. I was gratified when the new UA introduced versions of both of these with their feat revisions and things like weapon mastery and rogue’s cunning strike.
I tried the free feat at level 1 for a couple campaigns, and while players enjoy it, I find it tends to tip the game balance off a bit, such that lower CR encounters are a little underwhelming. You might not find it a problem in your games though, depending on how munchkin-y your players are.
Definitely agree martials need maneuvers - I highly recommend Laserllama’s martial homebrews for experienced players, gives those classes a lot more flavor and flexibility.