A complementary can should take into consideration your sonic preferances as well as application for system match to be effective.
The k701s as a referance can, being neutral and well balanced in their presentation also can be considered a relaxed warmer presentation than the 880s based upon my use of the 990s .
I'll throw in a can that has my interest. Have you considered the AT-AD2000?
But I do suggest you try the RS-2s for the experience of those strings played with details, attack & impact, without giving up the warmth and bass which seem to be a preferance of yours. Also, that they are a super easy can to get to sound great in a wide array of systems even mobil with a Shuffle should the ocassion arise...
While the 990s have the bass presence you seem fond of, they can indeed be bright in their midrange and trebel (recording dependant), and are much more a difficult can to get to sound pleasing, although mine are not going anywhere. I believe these qualities holds true with the 880s and I wouldn't simply buy it blindly thinking it would get headtime due to being so very different as to fulfil the role of a complementary can ...Nor does that mean it wouldn't be a good choice for some...
All higher level cans, even within the same basic signature, are so very subtly different in their presentation that they would be complementary providing something different to the same music played. I believe you are on the right track first identifying your prefered signature (with better than average bass), and venture close to that for other choices as a complementary can.
I'll throw in the AH-D2000s for your consideration also....
Unfortunately mine haven't arrived yet to warrant further thoughts on them. but what i have identified is that they too, like the RS-2 are easy to get to sound great not being tempermental as to downstream gears as other choices...
Hope this is helpful in your pusuit for a complementary headphone to your Darths