Does your feeder have corn in the seed mix? That attracts blackbirds/grackles and starlings. When I switched to black oil sunflowers, safflowers, and striped sunflowers, occasionally mixed with peanut chips, AND barricaded the feeder with wire mesh (about 1"x2") so that grackles can't get at the seeds, they stopped MOBBING my feeder. They still come but not as much and soon give up and go away. I guess the starlings follow grackles around because I have less starlings now too.
My neighbor throws out her breakfast bread and cereal left overs. They go to her yard. What they do that I can't stand though, is they bring their breads and cereals to "soak" in my birdbaths and fountain, creating a HUGE and moldy mess!
Now, I also have a feeder on the other side of the house which I only occasionally fill with a cheap mix containing corn and millet. The starlings/blackbirds/grackles as well as house sparrows visit that feeder.
So your idea to place *another* feeder at a good distance away may have similar effect as my neighbor's bread and my junk feeder....
What I consider as my MAIN feeder mainly attracts cardinals, chickadees, downy woodpecker, red bellied wood pecker, nuthatches, titmouse, and house finch.