Here's a “seating arrangement”
7 friends A,B,C,G,P,R,Y meet on $n\!$ = 7 evenings
Vertices ($\bullet$) = evenings.
Large labeled triangles = friends.
Small labeled triangles = outward-pointing corners of large triangles,
where they meet other triangles.
(Center vertex = first evening, where/when
the orange triangles A,B,C are the first three friends to meet.)
3 friends/triangles meet on/at each evening/vertex.
Each pair of evenings/vertices are connected by exactly one
friend / triangle-side.
No friend F can be present on 4 or more evenings because that would require
at least 4 other friends to be present on some other single evening.
(Some evening E is required where F is not present;
E is required to share a friend with each of F's 4 evenings,
but all other friends on F's 4 evenings would be different
from each other or else they'd be with F on two evenings.)
At most $n\!$ = 7 evenings remain in play.
(Each of the first 3 friends can be present on at most 2 other evenings.)
The light blue triangles show possible other friends, as long as their
extra corners can be connected back to the 6 perimeter vertices.
The solution unfolded with multiple images of each friend/triangle
so that all evenings/vertices can be seen.
(The nights/vertices are equivalent to a 7-colored torus.)