Filtered menu binding

I need to implement three dots … behaviour - when one want to select a proper value (person), he clicks on three dots, a new menu with values (e.g. addressbook) is opened and a user select desired person and clicks on “Select and return”.

The problem is my lookup uses filtered lookup list (e.g. choose one person from a people assigned to a project whose task I am standing on). Is it somehow possible to filter the bound menu the same way (pass the parameter about current project) and solve that situation?

The only possibility so far is to set AlwaysAllowReturnToForm = True. That will make the three dots appearing but the target screen will not get filtered.