Tripling of course is always better than doubling, but is it really necessary? Go ahead and do it if it's possible. However.....the only way to know for sure is if you find out what species and grade those joists are.
The answer you got before isn't really accurate. That deflecto tools is conservative (which is good), but only assumes you have Southern Yellow Pine or Douglas Fir, and doesn't distinguish timber grade. (which makes a big difference). It also does not tell us what live load-dead load it calculates. I do refer to it from time to time, but there are others that might give you a more accurate answer. Again, triple if you want to.
As far as CBU vs. Ditra. They'll both work if done right. I prefer Ditra because it will uncouple the tilework from the substrate, along with several other benefits over CBU's. As far as being newer...yes it's newer, but it's been out there for about 20 years, or so.
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The wife changed her mind and wants ceramic tile now so doubling the joists is all I'll need to do. Realistically, I won't be starting this project until 2009 but I needed the floor characteristics for the new stair case that I'm starting next week.
Thanks for everyone's help.