[quote=Ryu]
Let's rephrase this question of mine so it looks better and is easier to understand,

Can we have a character be taught in a less known style of Japanese Swordsmanship of Kenjutsu?
[/quote]

If I understood your question correctly, this should answer it. Both schools will have only one style to teach, as it should. However neither will be only the 'Basic' kendo. I will go fetch the exact and official names when I'll make the OOC, but I can tell you this now; ONe of the school will be about two swords fighting. The other will be about cutting with the blade, probably from the sheath, Zen meditation, Etc. 

@CoyoteKisses Really? I envy you! I always wanted to do this, but never actually found a school here to teach it. Or dojo. I sure welcome your help. ^^ Of course, since this is a RP, If you see I lack some terms at some point don't hesitate to teach them to me! Consider it a special demand. :P