I find in my yard that most of the non-aggresssive birds are happy to share a feeder. We commonly see Cardinals, House Finches and Rose-breasted Grosbeaks at one feeder...sometimes even more varieties. Most of the birds, though not all, will avoid the Blackbirds, including the Red-winged, unless there's food spread over a large area on the ground.
If you want to draw more Mourning Doves to your feeders, try a little Safflower seed in a tray-type feeder. They absolutely love it! Most of the time our Mourning Doves stay on the ground to feed, but it doesn't take long for them to discover the Safflower seed.
Safflower is kind of expensive, but I use it in small quantities once the Blackbirds arrive since it gives the more timid birds a place to eat without being bothered. The Blackbirds can't crack the hard shells so they leave it alone. Some birds may take a while to start eating it, but once they do, they'll go there regularly since the fatty seed is highly nutritious.
Here's a few pics from my yard and one from the nearby Fox River.