I interpreted your question to be an ironic gesture, so I didn’t felt equipped to answer, but I feel, that the answer is already implied in the question? Depending on whether you want a philosophical answer or a mathematical answer one could say:
Quantities, as you say, only relates to what is identical, you cannot have a quantity of dissimilar objects, so then, if I interpret your question correctly we can reformulate the question like this: does there exist identical objects in the manifested/physical reality? And if so what predicate must be satisfied for two things to be identical with each other? Should they be in a identical state aswell as having an identical kind or class?
Grassmann thinks is that discrete mathematics (dealing with different quantities (the integers) and their combinatorial relations) are ‘thought forms’. He calls the first part in the book ‘a theory of forms’
The name “theory of magnitude” is inappropriate for all of mathematics, since one finds no use for magnitude in a substantial branch of it, namely combination theory, and even in arithmetic only in an incidental sense.** On the other hand the expression “form” might seem rather too broad, and the name “thought form” more appropriate;
My interpretation here is that the word Magnitude stand in relation to what is manifested (comparable effect), a magnitude of weight for example is only intelligible by means of comparison to another weight, therefore it is not pure mathematics but something else.
Another concept to keep in mind is to understand what the virtual/possibility/contingency is, compared to what is manifest. I think that we can say that mathematics is more than simple contingencies, yet mathematics still shares the same nature of indeterminacy or self-sufficiency/unrelated-ness depending on how you approach the question. Lets us first understand the meaning of what a simple possibility / contingency is. In modal logic, a contingency / possibility refers to nothing more than the name and is determined only by that agent who gave ‘it’ a name, but cannot in an objective sense be associated with anything definite at all, not even a name. Guenon states it well:
The contingent being may be defined as one not having in itself its own sufficient reason;consequently, such a being is nothing* *in itself, and nothing of what it is belongs properly to it.
We can also say that this lack of sufficient information / its indeterminacy / its unrelatedness is what makes it in-actual. What I’m trying to say is that Mathematics shares this nature but is yet something more than just simple contingency. (depending on your outlook you could say it in a better way by focusing on the quality of self-sufficiency mathematics has in contrast to the inter-relatedness/fused togetherness that something manifest has depending on how you approach the question.) Mathematics can be seen to be working according to internally consistent rules on how to construct and operate with identity. Mathematics therefore can only have relation to actuality by what extent we give it a determining or attributing power to control what is actual. Like the math in a program that controls a robot for example. the math in itself has no information about the indefinitude of complex relationships that makes up the circuit board and the motors moving the robot, and even less so, everything that made it even actually possible to construct the robot in the first place. something possible/virtual, is so precisely because of its lack of sufficient information or interface for it to ‘act’ or have act-tual presence in our sensible reality, where everything is interrelated