In the picture, you see the longest roundtrip of a rook such that there are no "shortcuts" - imagine the target squares are given, then at each square you have exactly two other given squares accessible to the rook, and they connect to a round trip. (Trivially the longest rook trip length is 2*8.)
What are the values for the other officers? Q and N are most interesting. (I think I know the maximum for N.)
Note: a1-b1-c1 is forbidden, even if you can't go from a1 to c1 if something stands on b1.
Son of Note: You could formulate this problem far simpler: "Place m queens (knights,...) such that all queens are protected twice". But it's not the same problem anymore - the Qa6 will never "touch" Qh3.