  Bell state measurement is crucial to quantum information protocols, but it is
impossible to unambiguously distinguish all the Bell states encoded in
multi-photon using only linear optics. There is a maximum number of
distinguished Bell states, i.e. distinguising limit which is very important for
increasing the channel capacity of quantum communications. In this paper, we
separate $n$-photon $D$-dimensional hyperentanglement into two groups. For the
first group of $U$ ($G_1$), we obtain the limit ${N_1} = nD - (n - 1)$, which
can be applied for both bosons' and fermions' cases. We further discuss the
limit $N$ for any $nD$ system with the second group of $U$ ($G_2$), inferring
that at least ${D^{n - 1}}$ Bell states can be distinguished due to the
symmetry of Bell states. Obviously, ${N_1} \le {N_2}$ for those systems with
$n>2$. Finally, we theoretically design an optical setup for Bell state
measurement of two-photon eight-dimensional hyperentanglement of spin, path and
orbital angular momentum (OAM) and distinguish 15 classes of 64 Bell states.
Our results provide a theoretical basis and practical reference to increase the
channel capacity of the quantum communication.
