TBF the only class that gets more than one extra attack is the fighter.

Now of course it would make sense to sum up the levels you have in classes that get multiattack, and if you have >=5, you get an extra attack. But since attack progression is far less regular than spell slot progression, getting something approaching regularity beyond that would be difficult.

Now if OneD&D wanted to boost martials and introduce some sort of a multiattack scaling across multiclassing, here is how that could work:

1. Introduce features called Special Attack and Signature Attack. (Simply because just stacking extra attacks in a way that gives a bunch of half-casters extra attack at level 5-6 would give full martials a ridiculous number of attacks per turn at higher levels.) Special Attack is an attack that deals double weapon damage (which stacks with crits), but other extra damage sources like smites don't get doubled. Signature Attack is a Special Attack that can also force a save, either a STR save vs. being disarmed, a DEX save vs. being knocked prone, or a CON save vs. being dazed. You pick which one when you get the feature, and you can change it on level up.
2. Introduce an attack progression table which details how many regular and special attacks you get per warrior level. (IDK if Lemmy's MD syntax allows tables in lists, so see the table below.)
3. Like for spell slots, some classes (fighter, barbarian, monk) count as whole classes, others (paladin, ranger, artificer) count as half, and some caster subclasses (bladesinger, swords bard, hexblade, etc...) count as third.

The table:

So:

• A level 12 single class fighter gets 1 normal, 1 special, and 1 signature attacks.
• So does a fighter 6 / barbarian 6.
• A level 12 paladin counts as a level 6 warrior so they get a normal and a special attack. (Also, in OneD&D the divine smite is a bonus action spell like every other smite, so the level 18 paladin can't go too nuclear with 3 smites per turn.)
• A fighter 6 / paladin 6 counts as a level 9 warrior, 2 normal attacks and 1 special attack.

Of course this could be refined a bit further, e.g., instead of a generic "special attack" they could pick power attack (must be a strength-based attack), precise strike (must be a dexterity-based melee attack), or pinpoint shot (must be a dexterity-based ranged attack) and they could swap this one on level-ups too. But I think this should be a start.