Custom Color Over Multiplayer?

So I'm using a modified shader by Aubergine (I believe) that uses a color map to determine where color will be placed on the texture. The issue is, this only works for one instance. IE, player 1 selects green primary, red secondary. Player 2 selects red primary, green secondary. On player 1s client, players 1,2,3,4 etc all have green primary and red secondary, but on player 2s client, players 1,2,3,4 etc all have red primary and green secondary.

How do I save the color values and only apply them to the respective player, especially over a network?

I don't want to create a bunch of textures, because 1. That's texture loading overhead and most importantly 2. That limits the possible color combinations to whatever I make.