I currently have the Carcassonne base set plus Inns & Cathedrals which expands the game to 6 players. I've found that I can buy extra sets of Meeples in different colors which would effectively add additional players. Are there any potential downsides to doing this? Should I also get additional expansions to maintain some sort of "tiles per player" ratio?
You might want to consider getting another expansion or two -- with the base set plus Inns & Cathedrals, you'll have 90 tiles (72 core + 18 expansion) to play with. Assuming seven players, you'll have 12-13 tiles per person to play with.
Traders & Builders will give you an extra 24 tiles to play with, including some really funky shapes for finishing those hard-to-finish cities.
If you want to keep the game shorter, you can just use the two sets listed.
I have played with eight players using Inns & Cathedrals and Traders & Builders. Technically the game works fine, but the waiting between goes was horrendous.
Another thing to consider is that as the number of players increases, the game changes from being focused on clever placement of tiles to being more focused on negotiation skills. In my experience this also adds to the game length, as everyone wants to make a suggestion for every tile drawn.
An easy way to expand it without complicating it further with expansions (if that is what you want) is to simply add another base set into the bag at the point of 6+ players.
There are also a few promo expansions that just add a couple of tiles. Of course if you prefer expanding and adding more to the rules then expansions will suit just fine.