This problem is really hard, and I can only suggest that you should write a program to search for a workable solution. I think I would look for 32 interviews in the schedule (with 16 people) and I would try to rearrange the following 32 pairs and 32 triples so that all 5 people in an interview are different and all opponent pairs were covered at least once.
(1 2) (1 2 4)
(1 3) (1 5 7)
(1 13) (1 6 14)
(1 15) (1 8 16)
(2 9) (1 9 10)
(2 14) (1 11 12)
(2 16) (2 3 5)
(3 4) (2 6 8)
(3 4) (2 7 15)
(3 16) (2 10 11)
(4 5) (2 12 13)
(4 8) (3 6 10)
(5 6) (3 7 12)
(5 10) (3 8 14)
(5 16) (3 9 11)
(6 9) (3 13 15)
(6 12) (4 6 7)
(6 15) (4 9 12)
(7 8) (4 10 14)
(7 9) (4 11 15)
(7 10) (4 13 16)
(7 11) (5 6 13)
(8 11) (5 8 9)
(8 12) (5 11 14)
(9 10) (5 12 15)
(10 13) (6 11 16)
(11 12) (7 8 13)
(11 13) (7 14 16)
(12 14) (8 10 15)
(13 14) (9 13 14)
(14 15) (9 15 16)
(15 16) (10 12 16)