Second, I hang more than one box. Sometimes, two boxes at different heights in the same tree work well. The screech owl usually takes the lower box. Other times, hanging the boxes on opposite sides of adjoining trees works. Starlings in one box will actively exclude other starlings from using the immediate area.
Squirrels do the same.
Third, I use the starlings' and squirrels' own tactics - harassment. As are most birds, starlings are most easily disturbed while selecting a nest site, building the nest, and laying eggs. When I discover starlings in a box, I harass them mercilessly until they go away. Spray from a garden hose and tapping with a pole long enough to reach the box are useful. A half dozen daily episodes of harassment for two or three consecutive days usually suffice.