Is there any way to remove the 10 recipents limit from the SMS app? Can you actually do this? I know that there are some apps where you can send SMS to a unlimited number of recipients, but I would prefer to remove the limit of the built-in SMS app. My phone is a Samsung Galaxy Note II (rooted).
Since your phone is rooted you can use  Wanam Xposed 

Note that the framework itself doesn't add any functionality, but once installed you can download (via the framework itself) modules that have custom functionality. Wanam Xposed module has many tweaks for stock Samsung Touchwiz ROMs, GravityBox has many for morer 'stock' type ROMs. You can change the SMS limit through either, in the default SMS application. 

Please read the XDA Thread on this module as it has a lot of detail, and clarifications.
 XDA Thread