Maybe if you could apply multiple scores but have a cap on maximum bonus? I don't know.
A lot of the trouble in 3E (especially) and 4E (to a lesser extent) come from the insane bonuses given by ability scores. Quite frankly, getting more than a +4 bonus is going to break the game, because it's so out of whack with your lower scores.
D&D revolves around the tension between Attack, Defense, Hit Points and Damage.
In AD&D, Attack overwhelms Defense for physical attacks for the most part as you go up in levels (though PCs tend to get better defenses than most monsters at high levels), but Defense wins against Attack for magical spells. It needs to, because low-level magic is just variant damage spells, but high-level magic is "save or die".
In 3E, Attack overwhelms Defense for all attacks, except when you break one of the defenses. It was extremely easy to break AC - I had a couple of characters that on-CR creatures needed 20s to hit, although they could hit the bard and magic-users of the group on rolls of 2. The overwhelming of Defense was a much bigger problem in 3E due to "save or die" spells still being on the lists.
In 4E, Attack and Defense *mostly* keep up with each other, except for stat-pairs you don't care about. A cleric's Reflex save is laughable at high levels. At least there aren't so many "defend or suck" monster powers.
But 3E and 4E both suffer from the "I'm a thief with a high Dex, my Reflex is great!" but "I'm a thief with a low Wis, my Will is horrible." At higher levels, you're looking at a gap of 8 for those defenses *just from ability scores*. Given that the "good" defense is often hit about 50% of the time, the "bad" defense is hit 90% of the time. (3E is actually even worse: the gap can be between a 34 and an 8 at level 20, or a massive 13 in bonus value and thus defense score).
3E "dealt" with this problem by making the game into "get the right magic" - so Freedom of Movement, Death Ward, etc. are
required at higher levels just to stop all the Save or Suck spells, because no character has the ability scores to deal with all the attack types they might be hit by.
Limit ability bonuses to a maximum of +4 and you kill a lot of the problems the mathematics of the system throw up.
Cheers!