The standard model describes the particle's initial zoo into a smaller set. If I am not wrong quarks were proposed as a solution even before being detected. Is there any reason why we could not describe all the particles in the standard model as coming from a still smaller set? (ideally being described by a single generation of particles). Is there any obvious reason from group theory (or something else) that forbids this?
Note: I am not asking about experimental evidence, but rather, on symmetries and lie algebras, which I just started learning, regardless of if it will ever be possible to reach the energies to test it.