Any time I talk to someone who is inquiring about a Fender Twin Reverb or Super Verb (or the like) I always have to question what their use is for the amp is. Mostly because these are not bedroom amps... At 85 watts the Twin Reverb is a LOUD amp. With no master volume it becomes very difficuct to get the most out of these amps in practical settings... i.e. home studios, small practice spaces, or small gigs. They are GREAT clean amps... known for their clean tones and Fender reverb. That's really what they're known for and really where they shine. If you're looking for anything with grit that can be naturally overdriven - these aren't the amps for you. In most cases professional musicians will use these as their clean amps, but when they switch to an overdrive or distorted tone they will have a seperate rig with a different amp for that...
So, back to the whole "full" question... I imagine that volume is not your qualm with the Twin Reverb. I'm thinking you might be using the wrong amp entirely for the tone that you're looking for. When I think of a "full" sound I'm thinking of something that's the opposite as brittle... Equal response across all frequency ranges with good bottom end and nice clean top end.
With all that being said - Check out a Vox AC15 or AC30 (if you really need that much power). I think you might find the sound to be a bit less of a one trick pony and a bit "fuller".
I love, love, love Fender clean tones... my next amp will most certainly be a Fender Princeton. However, on more than one occasion I have talked myself out of buying a Twin Reverb simply becuase it's not a practical amp for studio uses.... I tried a lot of amps out and settled on the AC15 becuase it's power output is right where a studio/small gig tube amp should be. Gets loud enough for any practical band situation, has a master volume so you can clean it up at higher volumes or get it to break up at lower volumes, built in trem and reverb... Classic tone. That's where I would usually steer someone who thinks they need an 85 watt Fender Tube amp... haha. Unless they just love the clean sound - In which case, you cannot go wrong.