At http://www.mycolombianrecipes.com/three-milks-cake-torta-de-tres-leches is a recipe for 'Three Milks Cake' or 'Torta de Tres Leches':
Torta de Tres Leches or Three Milks Cake is a popular dessert in
Colombia and Latin America. This cake gets the name from the three
milks we use[:] condensed milk, evaporated milk and heavy cream and
[it is this that] makes this cake so moist and delicious.
The trouble with saying that this licenses the use of 'three milks' for 'three kinds of milk' more generally is that English is idiosyncratic. We'd say 'different allotropes (or polymorphs) of phosphorus', not 'different phosphoruses'. But 'different steels' is acceptable.
We'd certainly use 'three sugars' if talking about arabinose, xylose and sucrose, but rarely if ever if talking about caster sugar, demerara sugar and muscovado sugar.
The ratio of Google hits for "different musics" to "different styles / types of music" is about 1 : 40.
Again, considering portions / containers of ..., we might ask for two teas and three coffees, but surely not two waters and three milks - we'd revert to 'glasses of' here. But three milkshakes would be fine. Two beers and three lagers, yes, but two pints of mild and three pints of mixed.
So, we can't predict which usages should be / are considered acceptable, on the basis of analogy.