9. Iron Man
Tony Stark, with his mercurial genius, has more than a touch of Time Lord about him and it looks as if the Cybermen have been stealing his designs, too, if the flying metal men of Death in Heaven are anything to go by. Its not the first time Tonys tech has been misused and one cant help but muse if Missy used the art of seduction in order to get to his secrets. Stark could come looking for his lost tech and meet up with the Doctor. This clash of egos would be even bigger than the Doctor and Bond. Cue much comparing of sonic screwdrivers and repulsor beams before the pair team up to take on the evil Mandarin who turns out to be Anthony Ainleys Kalid from Time-Flight. Stark could also get a crafty look into the TARDIS which would set up the plot of Avengers 14 or 15, in which his home made transcendental engineering project threatens the world. The Doctor in an Avengers movie? Geek heaven.
Robert Downey, Jr is a fan of the show, after all...