Large rock obstructing addition
Bedrock - skip the basement, have the best foundation money can't buy. Remove the dirt, drill holes for pins to anchor your footings to the rock, build a house on it - or a skyscraper.

If you have more of a "fight with nature, rather than work with nature" approach, it's going to be harder, more expensive, and more tedious, and exactly what options you have and how dreadful they will be will depend on the rock - granite is rather more difficult than schist, for a couple typical NE USA bedrocks.