This is possible but there needs to be 9 rounds and 9 events - then each team has 8 intra-divisional games and 1 inter-divisional game and plays each event exactly once. In the schedule below division 1 is teams A to I, and division 2 is teams J to R, all the inter-divisional games are on the main diagonal. Because of the symmetry, rows and columns can be assigned to rounds and events either way. Hope that helps.
(A J) (Q R) (D I) (C G) (B H) (M N) (E F) (O P) (K L)
(H I) (B K) (N Q) (L O) (P R) (E G) (C D) (J M) (A F)
(M R) (E H) (C L) (P Q) (F I) (B D) (K O) (A G) (J N)
(L P) (C F) (G H) (D M) (J K) (A I) (N R) (B E) (O Q)
(K Q) (G I) (O R) (A B) (E N) (C H) (J L) (D F) (M P)
(D E) (N P) (K M) (J R) (L Q) (F O) (A H) (C I) (B G)
(N O) (L M) (B F) (E I) (A C) (J Q) (G P) (K R) (D H)
(F G) (A D) (J P) (K N) (M O) (L R) (B I) (H Q) (C E)
(B C) (J O) (A E) (F H) (D G) (K P) (M Q) (L N) (I R)
