Mixed Model with too many clusters

in relation to Gaussian quadrature inside stan?

I’d like to know what people do when there are too many clusters when doing Mixed model.

I know people just parameterise the individual clustering effect and do full bayesian analysis (prior -> likelihood -> posterior) but when there are too many clusters like over 100000 so that it will be too slow or would fit in a humble memory size of a personal computer, what would be the alternatives?