I think you have to look at it like this:
1) Is magic usable by anyone/everyone, or can only a small select few have the "gene" to us it? If the former, then go to #2. If the latter, then you have effectively kept magic from being used by the vast majority of the population, so you probably don't have to do any changing.
2) Are exceptionally high attributes (like 90+) needed to learn/use magic? If not, then go to #3. If so, then like #1 above, magic will still be rare and only those non-spellcasters who have the appropriate exceptional attribute(s) will be able to learn, but they still may not be allowed to learn.
3) Treat magic more like technology. As technology is used in our world, but just about everyone to one degree or another and pretty-much every profession (farmer, miller, thatcher, butcher, jeweler, blacksmith, etc...) will have their own specific magics they use to perform their craft. This is getting into Earthdawn territory so you could look to that for some inspiration, though Harry Turtledove's fantasy world war series could also be a great source of material.
Personally, I am of the opinion that for RM (any edition) non-spellcasters - including NPC peons - would learn 2-5 spells through their life. It does wonders for making a non-spellcaster viable at higher levels.