Note:This method requires the site admin to edit the user's profile after a profile type switch.
Create a profile form for a profile type. Eg: form A for profile type A
Add a multi choice field into the profile form. This can be checkboxes, dropdown list, multilist or radio custom field.
Make sure the Searchable option is enabled.
Add a few choice items into the custom field. These choices are basically your profile types.
Set profile type A as the default choice.
Disable all options in the visibility tab so that this field does not show up in the front-end for users to edit.
Repeat all the steps above, but now on form B for profile type B, set profile type B as the default choice.
Make sure the Unique Key for the field accross profile types is the same.
How it works
Users in the profile type with the above setup will have the default choice automatically selected and saved. When this field is selected during advanced search, the users with selected option(profile type) will show up in the results.
If a user is switched from profile type A to profile type B, site admin has to go to the back-end to edit this profile and set the field option to profile type B.