You should be OK to clear one super into the brood chamber - the bees will let you know by hanging out of the door if there isn't rooom for them, in which case you can out the super back on when it has been extracted.
Like most questions where Nationals are concerned much depends on what sort of bees you have.
You say one of your supers. What do you mean by full of bees? Is it workers cluttering the place up because of the weather, or brood? What are the other supers like, and more importantly what is in the brood box - is it full of bees, or are several of the frames being used for stores? Has the Queen slowed down her laying rate, in which case, how many frames of capped larvae are there?
If the brood is mainly full of stores, you can bruise these and thereby encourage the bees to move them to the super. This might leave enough room in the brood for any larvae.
But it is difficult to offer firm advice without more information.