  We show that arbitrarily high-order exceptional points (EPs) can be achieved
in a repulsively interacting two-species Bose gas in one dimension. By exactly
solving the non-Hermitian two-boson problem, we demonstrate the existence of
third-order EPs when the system is driven across the parity-time symmetry
breaking transition. We further address the fourth-order EPs with three bosons
and generalize the results to $N$-body system, where the EP order can be as
high as $N+1$. Physically, such high order originates from the intrinsic
ferromagnetic correlation in spinor bosons, which renders the entire system
collectively behave as a single huge spin. Moreover, we show how to create
ultra-sensitive spectral response around EPs via an interaction anisotropy in
different spin channels. Our work puts forward the possibility of atomic
sensors made from highly controllable ultracold gases.
