The best thing would be to use a different system. Failing that, perhaps the DM could remove "favoured class" altogether, and hence, allow for truly limitless multiclassing. Then again, some extra advantages for those who do so (multiclass like mad, that is) might need to be added on, as well.
And Dovahkiin would be more like a template, placed upon a race, rather than anything to do with classes.
Or simply "stuff" that is added to the PC(s) in question, when learned (etc.) - a setting-based special set of rules, in other worlds. That might be second best thing, actually. But in the end, Skyrim uses a skill-based system, and skills are improved by using them, then when you get enough skill upgrades, you gain a level. And so on - in other words,
nothing like D&D.
For Skyrim info, check this out:
http://www.uesp.net/wiki/Skyrim:Skyrim