I'm not entirely sure I have written a lot of Silver/Liz fic, but to my great joy and pleasure I have somehow caused a lot of Silver/Liz fic to be written, which is the best outcome, really.
(Well, actually, I probably have written a lot of Silver/Liz ficlets - 1 make it 4 out of 11, with 4 authors making up the total - but I would like to point out that most of mine were prompted by Pers, so I'm not sure which of us is mostly to blame for that.* ;-p OTOH, I think all of the others were written for me, so...)
Anyway, Liz/Silver was an accidental pairing that came up in a meme where you sorted your icons and paired them off, with fairly entertaining and improbable results, and then next thing you knew john_amend_all had written a ficlet, and then so had I... and then people were giving me Silver/Liz in fandom_stocking and the ship is a thing. \o/
I'm unsure how to answer this question, because this is me. I would put any DW character I felt capable of writing in a fic with Silver and Liz, so narrowing it down is hard!
Three or the Brig would be natural, given Liz's era and both would probably have a lot less patience for Silver than Liz does (in the fic; she is scientifically interested in him, he is a curious part of the universe that naturally she would like to explore), so that would be fun. (I feel Three, finding an Element, would be rather like a human discovering an unexpected rat or something. It'd be at least five episodes later before he could admit that one was okay and actually kind of interesting, he'd have to be locked up in a cell with Jo before he admitted that he found them unnerving, because different Time thingies.) The Brig could end up in a very bemused OT3 situation that he would never ever mention again. It did not happen. Liz humours him kindly. She has some sympathy for being bemused by Elements.
But then there is the whole wide universe of Doctor Who! I wouldn't put Adric in it (it would not be the sort of place Adric would be of any use, unless Silver and Liz needed some mathematical calculations doing, I suppose), and Dodo wouldn't be my first choice, and I can't claim to have watched The Dalek Masterplan enough to write much Katarina or Sara Kingdom, but otherwise the Whoniverse is pretty wide open.
Who do people think would be an interesting/good/hilarious addition to a Liz/Silver (or Liz & Silver fic)?
* Well, all right, me, probably. But Pers is definitely to blame for plenty of other things! ;-p (In the good way.)