Chickens can live on commercial chicken feed alone, as their diet. If you want them to be healthier and their eggs to be healthier for you to eat, then I'd give them some green feed. Dark green leafy plants to eat. The same things that are good for us to eat, to be healthier. For long term health, I think it's one of the best things you can do for your chickens.
Spinach, chard, kale, anything like that is really good for them and the chickens love it. Some greens grow well in hot weather and some in cold, even with a bit of snow. Chard grows well in cool and hot weather, so I'm especially fond of that here. Kale grows huge and is one of the most cold hardy. They also like different grasses. They'll actually eat a wide variety of plant leaves. They'll also eat most fruits and vegetables. Every year, we find out about more good things that fruits and vegetables contain. A grain based diet gives our bodies an unhealthy essential fatty acid balance, as well as animals, chickens and their eggs. Providing fresh leafy greens, helps with that.
I also provide more sunflower seed during molts.
If you can provide any access to insects for their diet, that's also very good for them.