Paths of unitary access to exceptional points

During the early history of unitary quantum theory Kato's exceptional points (EPs, a.k.a. non-Hermitian degeneracies) Hamiltonians $H(\lambda)$ did not play any significant role, mainly due to Stone theorem which firmly connected unitarity with Hermiticity. recent wave optimism people started believing that corridors a access EPs could be opened leading, say, new picture phase transitions via an {\it ad hoc} weakening Hermiticty (replaced by quasi-Hermiticity). Subsequently, pessimism prevailed (the paths appeared fragile). In way restricted physics closed systems return is advocated here: apparent fragility claimed follow from misinterpretation in its quasi-Hermitian formulation. Several perturbed versions realistic many-body Bose-Hubbard model are chosen for illustration purposes.