Given two identical particles, Wikipedia says that the wavefunction of a combined system where the first particle is in state $|n_1\rangle$ and the other one is in $|n_2\rangle$ is $|\psi\rangle=|n_1\rangle|n_2\rangle\pm |n_2\rangle|n_1\rangle$.
I assume that this is because you want $|\langle\psi|\psi\rangle|^2$ to be invariant under the exchange of particles. However, why not a more general $|\psi\rangle=|n_1\rangle|n_2\rangle + e^{i\phi}|n_2\rangle|n_1\rangle$?
There is a brief discussion on the fact that there are these exotic "anyons" that (I think) have these wavefunctions but why is it that bosons and fermions are the only common particles observed in nature? In other words, why are $\phi=0,\pi$ special?