There is the in-state vs out of state tuition distinction, so it's not exactly the same pool as east coast universities.
Sources: https://registrar.caltech.edu/records/enrollment-statistics https://www.collegefactual.com/colleges/massachusetts-instit....
These are interesting stats but they don't actually mean anything unless you can prove that the applicant pools for Caltech and Berkeley are similar to that of MIT. It's entirely possible, that Caltech and Berkeley have a higher proportion of Asian applications. It's also possible that underrepresented minorities that could be admitted to Caltech or Berkeley pick Harvard or Princeton because they're more well-regarded and more diverse. I wouldn't be surprised. Elite schools compete for the same kids.
Considering their ranking I would be willing to bet their applicant pool might significantly overlap (seeing as they attract world wide talent).
Are there any elite school (so sourcing students from the same pool of applicants) that don't include race in their admission process? Would be interesting to compare the demographics.