How many quantum numbers?
There is no universal answer, although for each system, one must find the answer for a full analysis of the system. The dynamics of any quantum system is described by a quantum Hamiltonian, H. There is one quantum number of the system corresponding to the energy, ie, the eigenvalue of the Hamiltonian. There is also one quantum number for each operator, O, which commutes with the Hamiltonian (ie, satisfies the relation OH = HO). These are all the quantum numbers that the system can have. In various fields of study, there may be slightly different conventions for writing the quantum numbers, although they can all be related to the definition given here.
