I couldn't find anything on this on the wiki, and there are too many results for "more than one housecarl"
here on the forums, so ..... can I get more than one? I know I can get multiple houses, but in the one game in which I did, I only got Lydia for a housecarl. Is it limited to just your first purchased house?

Getting a housecarl has to do with being a thane and not just buying property. Become thane in a hold where you can purchase property and you will also receive a Housecarl. Hope this helps.