Just a random thought to play with, develop, or throw away...
What about combining or averaging the "extra"/new abilities?
Take Strength and Dexterity -take the average of the score or the average of the bonuses or combine the bonuses outright or however you think makes the most sense = your Athletics score/bonus.
Intelligence and Wisdom combine [however] to = your Perception score/bonus.
Steeldragon, I second that Emotion steeldragon : (Empathy/Sympathy) (Wis/Cha) or Emotional Intelligence (Int/Cha).
In Jungian typological thought you can create four mental functions by combining Perception (Senses/ideas) and/or Judgment (analyis/decisions) with Intro and Extra, resulting in Pi, Pe, Je, Ji.
Pe - sensing the world and generating ideas/hypothesis
Pi - recalling information and personal reaction, and crafting theory
Ji - empathizing and analyzing
Je - sympathysing and executing
Divide P and J once apiece again and you have 8 mental function-pairs.
I love Julian Mays Galactic Mileu psionics, but it has 5 independent psionic traits (with almost an overall Mentral Stength score ala Gamma World), a and if you read descriptions of Julian's psionics in action you can easily see how the spell affects by the characters are actually combinations of the five different poles.
So I'm a big fan of combining the classic 6 dnd stats into novel combinations for such things as skill checks and saving throws. Plus it allows Int to be useful for more than one thing just for casters
I love the four square symmetry disco dichotomies of my system (yes, that was a typo with disco, but I love the nickname and I'm sticking to it). .In my psionics system 100 points are distributed amongst a two- by-two square along two axis - Introverted / Extraverted on one. And Telempathic/Telekinetic on the other.
You can manually distribute the scores or choose or 1d4 randomly distribute the d100. I haven't settled on whether TmE/TmI/TkE/TkI are created by an 'Additive combo' or 'Average combo,' or both for different purposes. I initially created this system 15 years before I discovered Jung and Myers Briggs and was struck by the parallel structures.
Success or Failure depends on a d100 roll of whatever spell/effect you're attempting. High TmE additive means you can charm from a greater distance, but the strength of the your charming is the average combo of Tm and E. Oh, and spend skills points for tricks based on character level.
Just more untested hypothetical systems to compare.