Create separate search forms for different post types?

We have been using Relevanssi to search for articles in a custom post type and so have limited Relevannsi to only index that post type and it’s taxonomies. Because it is the only thing indexed, the default WordPress search only shows results from that post type.

We now need to expand the scope of searches, in a different section of the site, to include all post types, pages and Woo Commerce products.

Is there a way to create separate search forms and results pages that search and show results from different sets of indexed content?

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