This demo site page shows how to use multiple search boxes on one page. View the to check the configuration.

The content groups are limited by the data-ss360-include="[]" attribute on the first search box and data-ss360-include="['Menu Items']" attribute on the second search box.

window.ss360Config = {
   siteId: 'spoonacular.com', /* Replace with your site id */
   searchBox: {
      selector: '.ss360-search-box' /* Replace with the css selector of your search box */
   },
   results: {
      embedConfig: {
         contentBlock: '.example__page-content-block'  /* Replace with the css selector of the DOM element you want to use */
      }
   }
};