The most microstates

 Back to the quantum shuffling game. By my calculation, this is the macrostate with the most microstates.

I tried to list all the possible states that began with 12 on Level 2. I found 6.

Then I realised that 13, 14, 15, 16 would follow the same pattern. As you start to put other numbers onto Level 2, you get some repeat patterns so the number of extra microstates falls. In the end, I think there are 76 possibilities.