Done this with vengeance and college of swords
5 levels Paladin + 5 levels bard (and 1 more level Paladin + bard, order doesn't really matter)
Potential problems: Build comes fully online only at level 10 (bardic inspiration resets on short rest, giving a lot of double smites)
The cost is a second feat only at level 9, not 8. No third feat. Would not recommend for lone wolf runs. This build basically builds upon the strengths the vengeance Paladin already has, but since they drop off after level 5, multiclass gives another major bump late game.
You don't really lose any important benefits long term except a 1d8 to smites. Having higher level spellslots than a pure Paladin and being quicker at depleting them more than makes up for it in my opinion.
There is a version which starts out as bard, then takes Paladin levels and works only really in combination with invisibility.
https://m.youtube.com/watch?v=0_tfO5w-0Hc&pp=ygUIYmFyZGFkaW4%3D
The go to for mutliclassing vengeance paladins is the Sorcadin, however. (For good reason. Not in the least: double hold person as a bonus action --> Band of the mystic scoundrel.)
What I personally don't like about such builds is that the smites are always competing for spells slots with everything else. What it does do is that it creates a character that is equally deadly no matter the distance, but that is only a boon if mobility is a major problem. The Investment for CC is more worth it, but I did do it to be contrarian. Also, it's not like I can't have an actual sorcerer for it in the party.
Vengeance paladins get their mobility at level 5, the same time they get multiattack. Going 2 levels Paladin, X everything else therefore majorly hurts not only your mobility, but pushes multiattack a lot further back (11). That means half the amount of smiting. You'll be rather reliant on items as well, because a Paladin is regretably incredibly slow.
But, because Paladins don't use charisma to smite, I'm not sure if a Paladin 5, cleric 2/3 dip wouldn't give you spirit guardians alongside better benefits. Do you really need 5 cleric levels, let alone 6 Bard levels? BG3 counts half casters in a weird way: it might just give you enough to unlock spirit guardians at levels 8. That's not fantastic, but the lore bard way only gets it at level 8, too. Might as well pocket something useful from a cleric subclass, like warding flare. Or war priest charges. If lore bard got multiattack, they'd have my vote since decent bonus action > reaction, but they don't.
Paladins are single target damage dealers. If you cast hold person or hold monster successfully, anything is dead. If it's not dead, try again with a monk as backup. Adding aoe is tempting, but there's usually a downside. However, Swords Bard 10, Paladin 2 gives you everything you asked for, except... you'll be in the middle of Act 3 by then. Start out as Paladin 5, switch at level 8 to Paladin 2, swords 6.
No cleric spells until level 12. Maybe bearable if you install one of the mods that makes the end game level 20 (either for real, or through mutliclassing only (so still only up to 12 levels in each pure class)). Add a diffulty mod. Aaand... The experiment is alive?
