Sarah Jane featured opposite Jon Pertwee and Tom Baker, guest starred with David Tennant twice, had both David Tennant and Matt Smith guest star on her show, and also was part of the Five Doctors special, where she shared the screen mostly with Jon Pertwee again, but briefly spent time opposite Peter Davison and Patrick Troughton, as well as Hartnell replacement Richard Hurndall. She also technically appeared with Colin Baker and Sylvester McCoy (as well as Jon, Tom and Peter) in the Dimensions in Time special, though she didn't actually share any scenes with either of them, so she didn't actually meet either of them, as such (and so doesn't really count).
Despite that, apart from Nicholas Courtenay as The Brig, Sarah Jane has worked with more Doctors on screen than anyone else. The Brig, of course, worked opposite Patrick, Jon, Tom, Peter, Colin (in Dimensions in Time), and Sylvester, as well as Hartnell replacement Richard Hurndall in Five Doctors. He actually starred opposite William Hartnell in The Dalek's Master Plan as well, just not as gold old Lethbridge-Stewart. I always found it a real shame that he was never asked to appear on the show proper when it came back, though he of course did make an appearance on SJC, and was mentioned by both the Tennant and Smith uncarnations of The Doctor.
I think if any other companions deserve to be made, after the various Doctors are done, and warrant it in terms of fan popularity, then it has to be Sarah Jane and The Brig.