Multiple InstantSearch Client with one Search box

Hello! Is it possible to create one SearchBox for two different InstantSearch components that are wrapped by InstantSearchSSRProvider?

I have to create a page in React 18 with Next.js 13 that contains a common SearchBox and 4 tabs (All, Tab1, Tab2, Tab3), where the All tab includes mixed info, 2 tabs - info from one Algolia search client and one tab from another Algolia search client.

I did this with react-instantsearch-dom lib by putting one InstantSearch inside another but now I’m rewriting the project with the latest React and react-instantsearch-hooks-web and that code not working anymore.