It appears that DW executive producer Steven Moffat had such a chance — and vetoed the idea of a season featuring individual stories for each Doctor and three team-ups!
The idea came up during production of “The Day of the Doctor,” when Smith and Tennant were thick as thieves. Moffat tells the story:
“They got on like a couple of old women. They just stayed in the corner and gossiped the entire time. By the end of it, Matt told me that he’d worked out a plan that they’d both continue in DOCTOR WHO: ‘Do five individual episodes each and three together – would that be okay?’ It was a nice plan. I think if I had said yes they’d have gone for it.”
Wow, my mind boggles at the possibilities of a shared Doctor season — especially with these two iconic and strongly delineated Doctors. Moffat was probably too far along with development of series eight, and Peter Capaldi was already on his way, so Moffat probably thought it best not to push things back an entire year.
But… still… another year of Smith? Another year of Tennant? Fangasm!