I always thought there were 10 parts, lol. Often, I've wished Nifflas gave us an arbitrary number of flags, such as 50, or 100, but there's probably a good reason why he didn't.
Luckily, there's a way to create switch-type conditions that don't rely on flags, so my levels have the illusion of having a lot more flag conditions, but such conditions are local to an area, and are forgotten when you travel a ways away (which suits the application just fine). This type also requires an entire region of rooms to be copied, and isn't really useful for the 13 objects dilemma, though.
Incidentally, you can also recycle flags.. If you pass through an area that you'll never return to, I'm sure you could re-use the flags in that area for different purposes, though I've never actually tried that. It would require planning and testing.
But I digress.... (yes, I do..)