They can run 12 all at once. My guess is that it is not very common that all 12 are operationally available and also needed. For example right now Montreal black is under the knife and is definitely not available for operational use. So assuming all the other trains are available they only have 11 that they can use. But 12 has happened.
It did happen this past December. It was the busy holiday season and I noticed the Epcot line was running four monorails. Honestly I'd never seen this before. Epcot used to consistently Run 3 monorails, now more often than not they run two, and occasionally when they're busy they go back to running three. So I was shocked but pleasently surprised in a fun way to see them running four. At the epcot station I inquired about the four trains and the monorail cast member proudly proclaimed they have a train dispatching every few minutes and also shared that it was a rare day where all 12 trains were running at the same time. 3-5-4.
I really could not verify that the express line had three in the resort line had five, but the Epcot line definitely had four. Gold, Coral, Red and Black. Even with four it was very smooth with no traffic holds and just cruised at speed to the TTC and back.
I was riding round trip just to see the construction at the Magic Kingdom toll plaza area. Yes, yes I'm a geek.