  Non-hermitian quantum systems can exhibit spectral degeneracies known as
exceptional points, where two or more eigenvectors coalesce, leading to a
non-diagonalizable Jordan block. It is known that symmetries can enhance the
abundance of exceptional points in non-interacting systems. Here, we
investigate the fate of such symmetry protected exceptional points in the
presence of a symmetry preserving interaction between fermions and find that,
(i) exceptional points are stable in the presence of the interaction. Their
propagation through the parameter space leads to the formation of
characteristic exceptional ``fans''. In addition, (ii) we identify a new source
for exceptional points which are only present due to the interaction. These
points emerge from diagonalizable degeneracies in the non-interacting case.
Beyond their creation and stability, (iii) we also find that exceptional points
can annihilate each other if they meet in parameter space with compatible
many-body states forming a third order exceptional point at the endpoint. These
phenomena are well captured by an ``exceptional perturbation theory'' starting
from a non-interacting Hamiltonian.
