A few do.
- There are three Allen Institutes (Brain Science, Cell Science, and AI), funded by Microsoft's Paul Allen in Seattle.
- The Gates Foundation (also funded by Microsoft, I guess) funds research, though mostly at existing institutes.
- The Howard Hughes Memorial Institute funds a bunch of research at its Janelia Farms Campus, plus provides lavish support investigators at universities.
- Eli and Ethyl Broad put up about $700M to endow the Broad Institute at Harvard/MIT.
- The Michael J Fox foundation funds a lot of Parkinson's Disease research.