Fundamental bosons, which are the mediators of the Standard Model interactions, are permitted to have multiple excitations with the same quantum number. Fermions, on the other hand, obey the Pauli exclusion principle, which reflects that they can only have a single field excitation with the same quantum numbers.
Composite bosons, such as Cooper pairs or pions, are composed of fermions. How can they have multiple excitations? This seems to imply that the constituent fermions also have identical quantum numbers, which is prohibited. Naively, I would expect these bosons to be the so-called "hardcore bosons".
