Remove specific projects from search results

We are using Elasticsearch to feed results to our GitLab code searches in GL v12.0.

For example, this simplified test search returns one hit in the “search_demo” project in my personal namespace:
https://example.com/search?scope=blobs&search=“Just+testing.”

In the real search, I want to remove some of the hits, per project. So in our example, I want to remove the “search_demo” project that had that one hit in the previous search. I might try to do it like this:
https://example.com/search?scope=blobs&search=“Just+testing.”+-search_demo

That does not work as it does not remove the “search_demo” project from the list of results for this search.

Is it possible to craft a search phrase that works the way I would like?

Thanks,

Rob.