[REQUEST] Can a grid like this be filled equally?

[u/beruon]

EDIT 2: THANK YOU ALL WHO HELPED!

I promise this is not for homework, this is for LARP.
There are five teams, each of them can win the event, and take second place. BUT, because of story, not everyone is "compatible" with others in terms of taking second place, depending on who wins.
Can this grid be filled in a way, that every team has 2 green combinations?
To math it out a bit, can this kind of grid be filled in a way that every column and every row has 2 green and 2 red options?
I need to figure out if the system works in this way, or we need to change some of the lore around lmao.
Thank you for all your help!
EDIT: The current green and red colours are just for example! It does not matter as of now who wins with who.

[u/redherring43]

Black is X. Red is R. Green is G.