I would hate being able to dual (or triple. Hell, I think by the end of Origins + DLC you could have four of the ****** things) spec again.
Specialisations are so powerful and change the way a class plays specifically because you can only have the one. If you could combine them they would get nerfed, hard.
I think mage combos would be mostly ok. There aren't a lot of crazy synergies that you wouldn't get with two separate party members. Most of mages' self-buffs are outside spec trees.
Warriors wouldn't have too many problems either, though I can see a Champion Reaver getting a little bit out of hand, because the benefits of each of those classes fill in the weaknesses of the other. It would be roughly equivalent to the "I have 15 million spellcasting pools!" Blood Mage Spirit Healer from DA:O.
But rogue combinations would be a little nuts, due to the large number of self-buffs in the spec trees.
An Artificer Assassin could guarantee criticals on all their biggest multi-hit abilities, without sacrificing dex or crit damage, thus lowering the long cooldowns on Mark of Death and Hidden Blades.
Tempest Artificer would never need to be outside of flasks. Flask of Lightning would provide enough crits to recharge Flask of Fire, and Throw Everything during Flask of Fire would recharge Flask of Lightning.
An Assassin Tempest could Flask of Fire then stack Mark of Death, which would vaporize everything. Instead of a 2x damage multiplier, they'd have a 16 or 32x multiplier, because every Mark of Death doubles the previous doubling. Plus guaranteed crits on Thousand Cuts.
It's self-buffs that cause the most balance problems for multi-specs. Everything else, eh, it's the same as bringing two separate party members with different specs.