Can I submit to the General CFP as well as to another sort of session?

Yes, but restrictions apply. Remember that for conferences (just as with journal submissions) each submission must be a unique piece of work. You cannot send the same paper proposal to the General CFP and to a Member-Organized or Joint-Sponsored Panel, and you cannot send more than one submission to the General CFP. You may send different paper proposals to individual CFPs, but you are restricted to having one paper on the ACCUTE program. In other words, if you are chosen for a Member-Organized or Joint-Sponsored Panel, your other submission will be withdrawn. Exceptions are made for executive-organized panels (such as the Board-Sponsored panels) and roundtables.  Another exception is the Christianity and Literature Study Group: you may appear on their program and on the larger ACCUTE program as well.