Introducing a whole new console doesn't make a lot of sense for Microsoft in my opinion. The performance gap of what, 30% maybe? Isn't really worth starting again with a customer base of zero and probably a much higher price.
If performance is a big concern of theirs, I'd just eventually start building xbox ones with slightly improved hardware to be on par with PS4. No need to market this as a brand new console or give it a different name; just sell it as a modernization of the xbox one, just like the xbox slim wasn't really a new console, but just a modification of the existing one.
Then, a crucial aspect would be to only allow games that fully support both the "old" Xbox one as well as the potential new one. All games can be played with the less powerful version, but the better one might offer similar features to PS4 versions (better resolution, higher framerates etc.).
To be fair though, I'm not really sure the performance difference is really the big, deciding problem xbox is having right now. It may be a very reasonable concern around here, but I'm not even sure the average gamer realizes its less powerful when making their purchase decision.
Take Apple, for example. While their products have some validity, I'd guess that >80% of their customers would, from a logical point of view, be better of with competitors' hardware in terms of pricing, speed and at times even functionality. But it's "cool", so people still get it and ignore most rational factors in that decision.
I'd blame a similar factor for Xbox, it just has a horifically terrible reputation. Probably mostly due to the xbox's nightmare pre-launch, e.g. DRM strategy, always-on kinect etc.). Plus of course a certain group effect, you'll want to play with your friends so you'll buy the same console as they're having, so it's somewhat of a self-reinforcing trend that will be more than difficult to break.