[RoundTower]

OK if this is what you mean:

you want to have four sets of 2 games, one after the other. Each player plays with each opponent exactly twice.

Spoiler in white:
<font color="white">I have a simple proof that this cannot be done. While this isn't much help for you organising your tournament, it is just as satisfying from a mathematical point of view.

Suppose A and B play together in rounds 1 and 2. Then at least one opponent must be in the game that does not include A and B, in both round 1 and 2. Call this opponent C. Now clearly A must play with C in rounds 3 and 4. But similarly B must play with C in rounds 3 and 4. Therefore A must play with B again.</font>

Hope this helps.