People have tried, but it isn't possible. Maybe, if you irradiate your hens with cosmic rays from beyond time and space it might be... I dunno
But egg color is about pigmentation or lack of it. Just as you have a skin that is of a homogenous basic color, so too the hen lays an egg that is the same basic color. Each hen lays her own color and doesn't have a palette of pigments to select from. The more closely aligned the flock is, genetically, the more unified the egg color from that group will be.
This is why commercial eggs are nearly all the same.
Commercial egg growers pick a breed known for very pale, ivory eggs (Leghorns) and then genetically select them over time to produce the lightest, even whitest, of eggs. It's what urban market buyers want. Brown and colored eggs don't go over well with urbanites, since white means clean and pure to most folks. It didnt used to be that way. It developed in the last 70 years, when it was apparent that the Leghorn is the MOST prolific egger in the smallest, most feed efficient size. Essentially, it came about as result of production economics.
On a side note, meat chickens intended for market sale in the US are bred for a white skin - without any black plumage to taint the feather pores - for the same reasons.
But none of this stuff applies to your typical backyard flock, with its normal genetic hodgepodge. EE'ers and many of the birds foisted off as 'Americana's are indeed mutts, as someone said. They are bred only because they give a colored egg, other traits notwithstanding.
In the small flock, the intensity of egg color can vary depending on many things, not the least of which is
Breeding
Diet
Laying cycle
Individual bird
Stressors (Im guessing at this one, since some birds of my past experience gave varying hue intensties for no reason I could determine.)
But, regardless, the color of each hens eggs will remain basically the same throughout her life.