That's a common issue with those sorts of birds and any really good resources, they try to keep them for themselves and drive everyone else away. If you want to provide for the smaller birds too you need to have smaller bird baths and flowering plants that provide some nectar but not too much - anything too good the big aggressive birds bully them away from. That's one of the main things I've learned so far from by Backyard Biodiversity subject.

That's what happened in my back yard too. I set up a birdbath and within a disappointingly short space of time, I'm talking about an hour, I had those Indian Myna birds bullying away all the birds I sought to attract. Not wanting those pests to set up camp, I relocated it to the side way where it is now a very shallow bee drinking station (too much human activity in close proximity for birds so they don't use it).