From my understanding of your approach, this is somewhat reminescent of the D&D 4E Hybrid class system. If you are not familiar with it, you might want to have a look. I thought it was relatively well done. In essence, they 4E Hybrid class system gives a list of abilities you gain at each level when you are levelling up two classes at once. So you start as, say, a fighter-wizard 1/1 from the get-go, and you gain 1/2 HPs from the wiz class, 1/2 from the fighter class; then you split the powers you normally gain in a single class, into two classes; and then all class-specific features you do gain when you take on two hybrid classes are listed. The end result is very balanced, I've tried it out; in fact the PCs are probably very slightly weaker, but have of course more versatility.
So in this case, what you could do is make half-classes for all classes including the human and non-human classes. Anyone who takes on two classes, be that a human that becomes a fighter-wizard or a halfling that becomes a wizard, would benefit from the abilities of each of his half-classes. For example, at level 1, the class progression could look like this:
1d6 HPs divided by 2 (keep fraction, but round down after HPs are added with those of other half-class)
2 spells known
Maximum spellburn = 1+Stamina modifier
1d4 HPs divided by 2 (keep fraction, but round down after HPs are added with those of other half-class)
etc... (anything a class gets, give half; for saving throws, if the class normally gets +1 on two different saves, only give +1 on a single save, and so on)
On at least a few things, you need to round down, otherwise multiclassing becomes the better option. I think that versatility should come at a price, but that's my preference.
Once the list is done, anyone can multiclass, although demi-humans could only take one a single other class as their race counts as class at the outset.
Maledict Brothbreath, level 4 warrior, STR 16 (+2) AGI 7 (-1) STA 12 PER 9 INT 10 LUCK 15 (+1), AC: 16 Refl: +1 Fort: +2 Will: +1; lawful; Armor of the Lion and Lily's Blade.
Brother Sufferus, level 4 cleric, STR 13 (+1) AGI 15 (+1) STA 11 PER 13 (+1) INT 10 LUCK 9, AC: 11 (13 if wounded, 15 if down to half hit points), Refl: +3 Fort: +2 Will: +3, chaotic, Robe of the Faith, Scourge of the Maimed One, Darts of Pain.