Could you please be more descriptive?
What type of content are you searching? Posts, pages, custom post types, terms..?
Which fields are concerned? Title, content, excerpt, custom fields?
Can you provide an url to a test or staging environment and backend + ftp details so I can run tests regarding the problem?
Can you also provide examples of the problem? (which keywords should return which results, etc..)
If the fulltext is not available, it's a good sign – since keyword logic is won't work in fulltext search mode. It's all right if fulltext is not available, it's not required at all. Most database hosts are not using it anymore.Best,
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