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In theory, there should be a straightforward generalization to multilevel data structures that yields results similar to generalized estimating equations after integrating over the random intercepts.

However, the example of double-weighting provided in Savitsky and Williams (2022) is done in the context of a centered parameterization (see appendix C in their manuscript) and I am admittedly not entirely sure how to code up an implementation that would be compatible with brms which only supports non-centered parameterizations for the group level effects.

I'll give this some more thought tomorrow but we will probably need to ask the Stan folks about this one. Opening an issue here to keep it on my todo list.