I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on.
"Derived quantities" have dimensions that can be written in terms of the dimensions of fundamental quantities.
Let us say that I have a chemical simulation that takes into account the number of particles of a particular agent -- "moles". There is a relationship between the number of moles and the mass of the particles, so in this scenario I would say that moles are a derived quantity?
What if I am working with a model where the number of particles is a much nicer number to work with than the mass of the particles (for e.g. proteins on the order of hundreds of thousands, but not on the scale of Avagadro's number). Is the number of particles then a fundamental quantity in this context?
More specifically, let's say I am working with a model that considers forces at the level of a cell (say, forces on the order of nanonewtons being exerted by various agents on the cell membrane), while also tracking a small number of proteins.
Would it then make sense for me to have two fundamental quantities -- one being mass in the mechanics calculations necessary for cell level effects, and the other being "number of particles" necessary for "mass law" type ODEs desribing the interaction between proteins?