Six is currently the maximum. This is comprised of three'a the five standard-fare Challenges (Unevolved/Scramble/Moveset), one of the remaining two (Single or Monotype; both are team-size specific and thus incompatible), the sole official intermediate Challenge (No Item), and Nuzlocke. Harmonia will only be compatible with No Item once the Ruleset is made official, so don't concern yourself with it.
I didn't include Moveset in my five-way Combined 'cause I sure as shit wouldn't trust anyone but myself t' give a proper moveset for what is essentially the most difficult Challenge... that, and I'd rather blame myself than someone else if I were t' of failed any amount'a times. I was hesitant to do Scramble as well, but it was either that or Moveset if I wanted t' secure said bragging rights for a time.