This is entirely possible but mostly frowned upon by broadcasters because running 2 HD signals at once degrades the overall picture quality for both because of the bandwidth both HD channels will use.
ABC O&O's have been running their Live Well HD subchannel for a few years now.
ABC will be pulling the plug on the Live Well subchannel any day now because of zero interest.
That said, from an over-the-air standpoint the PQ on the main ABC channel (at least in the case of KABC-Los Angeles) there is some noticeable PQ degradation on shows where there is a lot of fast motion and action.
Not only that KABC runs two LiveWell subchannels; One in HD & SD which is an exercise in absolute futility and pointless redundancy.