Maybe adding a new genetic, not in colours but in how special a base is,
for example; Common; Special; Rare.

I noticed at some point its very easy to breed cameo bases, like you could have 5 litters with a cameo base parent or possibility and you could have 1 cameo in 4 of the 5 litters you bred.
But then you could try to breed with a cherry-blossom base or sunset but get only 1 cub (or none) in 1 out of maybe 20 or 30 litters.
And both are in the special category.

So to give bases that are very very difficult to breed a rare tag instead of special.