Multiple keyboard handlers at same time? (RadioGroup + ComboBox)

[JacobJaffe]

Hi, is it possible to compose RadioGroup and ComboBox in such a way that the Up/Down keys can be used to navigate the ComboBox, while the Left/Right keys can control the RadioGroup?

I would like to imitate the behavior of the Vercel Doc's search bar:

Here the pills (All , Vercel , Next.js, Turborepo) are navigable with Left/Right, and the Search Results are navigable by Up/Down. At the same time!