Quantity theory of money: microfoundations
In the chapter 4 of the graduate textbook  Lectures on Macroeconomics there is "The Overlapping Generation with Money". In that case we have a model which is microfounded (i.e. accounts for how our consumers interact with money on the microeconomic level). This is essentially an explanation of Paul Samuelson's 1958 "consumption loan model".

You can find a useful set of videos on this model here:
https://www.youtube.com/playlist?list=PL10zuK3j9SNl15Xy-EGteGDTd74j4uE_n