First, structural damage to the house, cracked plaster, un-square doors and windows, etc.
Next, price verse value. The money you spend might increase the living space for you, but it won't necessarily increase the living space for appraisal value like an addition or above grade improvements would.
Third, exterior and additional costs. If you do this, will you then have to replace any plumbing or sewer lines? Will you have to re-sod the yard after all the heavy equipment destroys it?
And last, a bit of advice I heard was, "whether you are moving a house one inch or one thousand miles, get a certified home mover to do the job." There aren't a lot of those companies and they are expensive.
My advice, buy a larger older home and forget about the basement.