Part 61/AC 61 isn't very specific about does the flight tests except an 'appropriately qualified flight examiner'.
As far as I'm aware the initial issue has to be done with ASL. If this is in a single engine aircraft then the conditions stipulated in your logbook sticker when you pass will be for single engine or centerline thrust use only. Then this can be upgraded to a multi-engine, non-centerline thrust aircraft by doing a check flight with a GA examiner.
This is what I did.