InMemoryDataProvider.addFilter() alternative for BackEndDataProvider

I’m attempting to do something that is very simple with a DataProvider such as ListDataProvider, but I cannot figure out how to do with an implementation of a BackEndDataProvider. I am essentially trying to duplicate the result from the first example for filtering a grid at, where the grid filters the data down based on multiple queries. Due to the lack of the far easier to use addFilter() method I’m hitting a huge roadblock in my ability to do this.

Is there a standard way to go about this? An extremely similar question was asked here some months ago, solving their problem would solve mine.