The primary purpose of the calendar system is for keeping track of the world's timeline, but to do so in as con-culture-y a way as reasonably possible. That won't really be compatible with discontinuous calendars, although I'm sure you could find a way to simulate such a thing just by marking dates on a continuous calendar. (It's good to know that kind of thing exists, though!)
Systems with no week won't be a problem—hopefully the core features of the Mayan system will be fully implementable.
“An example of one of the ways in which you shouldn't start sentences is that this is a terrible sentence no one wants to read. Seriously, if you ever start a sentence like that, you’re fired. Clean out your desk. Go.”