Quantity theory of money: microfoundations

The quantity theory of money states the price level is proportional to the amount of money in circulation. That is, if the quantity of money increases by some factor $$k$$, the price level will increase by the same factor $$k$$. My question is simple: in which economic models should one expect such a claim to hold true?

To be clear, I am asking about 'microfounded' models which contain full descriptions of the preferences and constraints of the underlying agents (including but not restricted to general equilibrium models). I am not interested in equations like $$MV = PY$$ unless you can show that they arise from such a model.