It can be done both for the Autocomplete and the Instant Search results page in a few steps.
You can follow our multi-categories autocomplete tutorial that explains how to perform the same query on multiple indices and display results in the same auto-completion search box.
If you have built your implementation with the JS Helper, you can use the derive feature. This creates a new JS Helper synced on the main helper on which you can add event listeners to update the parts of the UI that use the sub helper.
It is not yet supported natively in instantsearch.js nor in react-instantsearch. If you’re interested in this feature, raise your voice in the github project.
Searching on N indices will generate N search operations, which has an impact on the pricing.
We're always looking for advice to help improve our documentation! Please let us know what's working (or what's not!) - we're constantly iterating thanks to the feedback we receive.