Basement / foundation - adding 1200 sq ft to our house

We are fortunate enough to buy a house in RockRidge in Oakland a couple of years ago.  The house needed substantial amount of work, most of which we've completed.  One big project remains, which is redoing our foundation / basement, digging a couple of feet, and making that space livable, essentially adding 1,200 sq. ft. to the house.  Before we bought the house, we had a couple of contractors walk through who gave us general round quotes (the quote was roughly $500/sq ft).  I recognize that prices have gone up in the last two years (though lumber prices are actually back down to 2019 levels after more than doubling in 2020/2021) - but now the same contractor is quoting me $900/sq ft - $1,000/sq ftand the actual size of the space is bigger than we eye-balled during that first walk through (now we have drawings done / permits pulled, etc.).  This doubles the initial estimate - which we can't afford. We are thinking of perhaps using two contractors:  1 for the foundation / basement dig out and one for the framing / finishing (so that we don't have to pay the overhead on the first part of the work to the overall contractor).  Has anyone done that?  Also, what is the overhead these days (my contractor is proposing 20% which seems high).  If you have done similar work, do you have any recommendations for contractors who handle these types of bigger projects?  Many thanks.