If I am calculating the molarity of a solution in which more than one solute is dissolved, can I add the total number of moles of all the solutes together and divide it by the total volume of solvent to get the molarity of my solution?
It doesn't make sense to add the total number of moles then divide by volume to find molarity. By doing that you are assuming that all the solutes have the same concentration which is not true(you are finding an average concentration of the solution but it's not necessarily correct). The solution contains different solutes at different concentrations. I think what you're doing only works if you know that the concentrations of solutes in the solution are the same.