Plugin Tag፥ search plugin
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Stop Search Spam
The plugin blocks internal site search spam (what lowers your site's ranking in the Google).
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i-Search – Advanced Live Search
Live search suggestions for all post types. Search everywhere, include almost everything in the search. WooCommerce compatible.
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Smart Searchify
Smart Searchify enhances the search functionality of your WordPress website to next level.
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WDV Ajax Search
With this plugin you can create different search forms for different post types and put their shortcode on the corresponding page.