It seems possible to make a Shopify Search & Discovery app and add filters. But you say you don’t want to use an add-on.
You can also try this option.
To autocomplete the school search field, you must create a custom field that will auto-suggest suggestions. In the Shopify admin panel, go to “Settings” and select “Search preferences”. Create a new “Custom field” named “School” (or whatever you like). Customize the field type for autocomplete or dropdown list. Populate this list with the values of all available schools so that visitors can select the one they want.
To allow the visitor to see the available tools in the selected school, you will need to create pages for each teacher with information about the tools and link them to the respective school. Find “Theme options” or “Customize theme” in the admin panel. Create a new page for each teacher, add information about the tools, and tag the school. Customize the display of pages with information about teachers by tag corresponding to the selected school. This can be done using the “Collection customization” section or sections. When submitting the form on the school selection page, visitors will see a page with the results of teachers who belong to the selected school and use the selected tool.
I think some of the steps may differ depending on the Shopify theme, and may require some tweaking with HTML, CSS, or JavaScript to get a certain look and feel.
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