Prefer: profile="[ogc-rel:results]" (or its long form with https://www.opengis.net/dev/profile/OGC/0/ogc-results) could be used to specify the desired profile.
The Accept-Profile header, Prefer: profile and ?profile= query are provided for the time being.
However, Prefer would require a response Preference-Applied header to indicate it was resolved this way in order to comply with usual Prefer behavior.