Billie Cantwell and Liz Cutrone at Knoxville's Wildbirds Unlimited, I adjusted a Dinner Bell feeder to exclude larger birds by lowering the dome cover to a few inches above the tray, filled the tray with smooth "butter bark" suet pellets, small home-made suet crumbs and freeze-dried mealworms and hung it near the bluebird feeder. When the male bluebird came to the feeder, his companions soon discovered the added food source and were also able to eat from it. In their absence, I noticed the Hermit Thrush landing on the dinner bell also to eat suet.
Additional good advice-- spread your suet feeders out so if a larger bird claims one feeder, there is an alternate area for the smaller birds to visit.
In the spring you can also consider planting Sumac near the borders of your yard. In Pitts' studies in northwest Tennessee, two native species, smooth sumac and winged sumac, were the most favored fruit of bluebirds, composing 50-90% of their winter diet even when a variety of other fruits were available.