There would have to be 28 rounds in order for every team to play each other at all games - that does sound too much. For anything smaller you need to decide between having every team play each game the same number of times (any multiple of 4 rounds), and having every team play every other team the same number of times (any multiple of 7 rounds). The following schedule gives you two possibilites.
Game1 Game2 Game3 Game4
R1 (3 8) (1 2) (4 7) (5 6)
R2 (6 7) (4 2) (5 8) (1 3)
R3 (6 2) (5 3) (1 4) (7 8)
R4 (1 5) (6 4) (7 3) (8 2)
R5 (8 4) (7 5) (1 6) (2 3)
R6 (3 4) (8 6) (2 5) (1 7)
R7 (2 7) (1 8) (3 6) (4 5)
R8 (1 5) (3 7) (2 8) (4 6)
play rounds 1 to 7 to have every team play each other once, or play all 8 rounds to have each team play each game twice.
