Hello, Ljorgie, this is an older thread, and I haven't read it, so starting here; where about are you located? Hot climate, cold, temperate? It matters. Are old your current birds, and are they all females?
Many breed types will work, although there are some who may be more difficult.
Production reds, which includes those 'orange' Rhode Island Reds from hatcheries, all tend to be bad at feather picking and harassing their flockmates. They are good laying hens for a year or maybe two, but can be disruptive.
Salmon Favorelles are very sweet birds, sometimes too timid to cope in a mixed breed flock. Definitely not with production reds! I think they do best in a flock all their own.
For fun egg colors, try some Easter Eggers, and maybe brown Leghorns too. Then Speckled Sussex, Wyandottes in so many colors, Chanteclers if you are in a colder climate, or any single combed breeds in hot climates.
Henderson's breed chart is really helpful. For rare breeds, look at the American Livestock Breed Conservancy. For more photos, feathersite and the poultry catalogs.
Have fun!
Mary