I haven't found a definitive 'no' but with a bit of quick googling - the current mission extension runs until (at least) 2021 and there is very little onboard fuel for significant course updates. Some of the other potential targets were in fact ruled out by the selection of Ultima Thule. The extended mission for New Horizons calls for the spacecraft to conduct observations of, and look for ring systems around, between 25 and 35 different KBOs.