If there's a language rule that says you can't combine these two this way, I'd be more than happy to learn about it. English is not my mother language so I apologize for any grammar/spelling mistakes in advance ;-)
There's definitely no rule against it. I wouldn't think anything of hearing "who're" everyday conversation. It's rare you see it in writing, though.
What you hear in every day speech is governed more by the mechanics of how your mouth works when you're speaking fluently, honestly. For example, if I were to say, "I would have done it" it most likely would come out sounding like "I'd've done it." Unless your intention was to get the sound across, though, you'd never, ever write that.
Uncommon, sure, but still correct. Myself, I like "who'd've" and similar. Never seen in written English, but quite common in spoken English. Who'd've thought you could put two apostrophes in the one contraction? :)
> Who'd've thought you could put two apostrophes in the one contraction?
Yes, and perhaps more interestingly, what will it look like 500 years from now? Many common modern words that we assume to be self-contained turn out to be pastiches of two or more older words. Like "shire reeve" -> sheriff.