Hi Alessandro,
Well, the instances are indeed shared, but problems can arise whenever there are some advanced features in use – like category/term exclusions, filters etc.. – as most of these objects are not shared across the multisite blogs.
If the network is not too big, this should be the best solution. If one single search instance can handle all requirements, and the only issue is the language of the labels, then it is possible actually to translate the labels using PolyLang or WPML string translations: https://wpdreams.gitbooks.io/ajax-search-pro-documentation/content/translating_components.html
Best,Ernest Marcinko
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