The core classes themselves would not have so much Greyhawk built into them, or even so much 'Pseudo-Medieval' built into them. Thus, fighters would just be people who fight best, where the feats you pick determine if you wear armor, or are a monk, or a barbarian. Experts are the skill guys who win by out-thinking the enemy, but that can mean you're an inspiring bard, or a sneaky back-stabber, or a monster-hunting scholar.
Mages could be updated easily to keep core D&D sacred cows while making multi-classing work. Spells would be divided up into traditions (with the 3 samples being wizardry, clerical, and naturalistic, though gamers could easily create new ones). Whenever you level up you can pick spells that you know from whichever tradition you're leveling up in. Choosing spells of a certain level in a particular tradition have a prerequisite number of ranks of Knowledge (tradition), so dabbling in two traditions isn't that hard to do, but dabbling in lots can be hard.
The ability to cast spells you don't know by preparing them in advance will be a feat, so you can still make a classical wizard.
The Player's Handbook should have a chapter, at least 10 pages long, on how you can use the same classes to create different types of concepts, for different classic fantasy archetypes, or for exotic things like Arabian, Japanese, or Planescapian.
Options, not restrictions. Reduce the number of mandatory rules, but provide lots of examples of them in use, so people can create the type of game they want.
