With the current configuration, there is no ability to create a new "Lookup view" and configure multiple settings and use them differently.

Therefore, it is easier for some users to have multiple "Lookup views".

This is because when you refer to the child entity from each entity in the search field, the items you want to check are different for each main entity.

It would be more convenient to save the "Lookup view" set up like a view and modify it according to the purpose.