If I remember right, there is a conflict with the two being mounted at the same time. But some clever modification of either or both parts may let you do it.
A little practice and trial and error when you mount the MMM will give you a good idea what must happen next.
I know on my X485, the front quick hitch for the blade uses the same holes in the 'tractor' plates as the MMM front 'bail' uses. So both attachments cannot share the same hole, so to speak. But you are right, there are times when grabbing the blade without dropping the deck would be very handy and worthwhile.
Quickly grabbing the FEL to do the blade chores might be handy and possible with the MMM still attached.