Fitting a beta-binomial model in the case of overdispersion in R

I'm estimating some count data. I have counts for say $m=100$ individuals. Unfortunately when using the Poisson regression overdispersion occurs. So I was thinking to fit a negbin model. But this is not appropriate in my case. So I assume that I can not fit a Poisson regression, because the way the Poisson distribution arises is not appropriate in my case ($n$ is not growing to infinity and $p$ is not converging to zero). So I found the beta-bin model. But quite honestly I'm absolutely not familiar in estimating beta-binomial models using R?

First of all: Does it make sense to fit a beta-bin model when anyone wants to estimate counts? Btw: If it makes sense, does anybody know a good book where the application is discribed?

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