I think the schedule below should work. In the first part above the dashed line, each team gets exactly 3 games. Then in the second part, if team A is not going to play teams B and C, then leave out (A C) and (A B) at the end.
(E G) (D H) (C F)
(B E) (A F) (C D)
(A G) (C E) (B H)
(F H) (A D) (B G)
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(B F) (D G) (C H)
(A E) (G H) (B C)
(E F) (B D) (A H)
(D F) (E H) (C G)
(D E) (F G) (A C)
(A B) (---) (---)