I can see my profile from the perspective of a 1st level friend, but I would like to see how my profile looks for a specific friend of a friend, or even from a general "friends of friends" perspective.
Is this possible?
You can view from a public perspective or a friend's perspective - but not from a friend of friend's perspective.
To do this, head over to your profile page & Click on View as...
Note: This answer is assuming you have the timeline view enabled