Is there any way to add internal search to a password protected site

We are building a password protected site for a non-profit with 2500 members.  We would like to offer members the ability to search for content on the site while they are logged in.  Squarespace search does not work well and it is my understanding that none of the plugins (such as Elfsight) will work as they rely on Google search and Google Search will (or can) not search password protected sites/pages.  Can anyone recommend a solution or a plugin/. Tx.

The search I know is Elfsight and Universal Filter Plugin, you can find this plugin.

Thanks Tuanphan.  We are planning to use Elfsight, but you have the same issue with it not working on a password protected Squarespace site as it also uses Google Search under the hood.