At least in the US, an institution’s “facilities and administrative” F&A rate gets negotiated with the Federal government every four or five years.
I know of some institutions with F&A rates at or above 70%!! I presume that an institution trying to negotiate a higher F&A rate than this would have some significant pushback!
70% is not that high these days -- there are institutions (normally non-university-affiliated research institutions like the Salk Institute that still apply for NIH and NSF grants) have overheads of 90%! It's important to realize that overheads aren't taken out of the grant given to the researcher, they are added to it. So if a researcher gets a $100K grant at institution with 70% overhead, the institution gets $170K.
Many grant giving institutions limit what they are willing to pay. For example, from my understanding the European research council will only pay 25% even if you university demands more.
I saw them take 60% as overhead at one of my institutions.