Yes and no, but mostly no
as mentioned, typically the best you can do is select for the darkest blue and work forward, but it could be that your flock does not have the potential for deeper blue so you might want to bring in some new genetics to your flock.
But, the thing about mixing in green egg layers to improve blue eggs, is that the pigments that are responsible for blue and brown eggs are different pigments caused by different genes, and green egg layers have both. Which means it’s going to be nearly impossible for you to select out the brown egg genes, so that you would end up with blue not green.
This is because there are multiple genes at play when it comes to brown eggs... which means that selecting to remove the brown egg genes from green egg laying lines is difficult and is often a two steps forward, one step back process.
So generally speaking it would take a very large number of chickens to select from and a lot of years to move forward toward better blue eggs by mixing in green egg lines... and
most likely no matter what you did, you’d end up with eggs that are green not blue.
There is a lot of misinformation about blue and green egg color out there and much of it is here on BYC. And some of this is due to the fact that much of it is still not fully understood, and some of it is due to the fact that the genetics involved are complex... but hopefully I haven’t contributed to that, but that’s my attempt at a “short version” explanation
Btw, I’ve had Splash Ameraucanas from Cackle Hatchery that laid better that average blue eggs... just in case ordering new chicks is an option for you... but I’d think that would be a better path toward better blue eggs.
