Thanks for your reply, Abe! I, too, thought that I was allowed $5500 max for ANY and ALL Roth accounts (combined). To clarify, I consulted with a TIAA-CREF rep last month because I was interested in upping my contribution to the university-required fund. Apparently, though, that's not allowed; when we want to add additional funds, we have to open a supplemental account. The rep said that I could have a supplemental Roth in the 403b plan (which could be in any fund/s) and put up to $17,500 per year in (even in a Roth) with post-tax money.
My initial response was "Woo hoo!" but now I'm not sure if it wouldn't be better for me to open up my own fund directly with Vanguard. Regardless, I obviously need to ask more questions of the TIAA-CREF rep re: how the supplemental plan works, especially in relation to a Roth (and he was clear that I had my own Roth that I max out yearly)!