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Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet ofbosons described by the three-parametric Bose-Hubbard Hamiltonian$H(\gamma,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$and $\gamma \to v$, as an unperturbed part of the family of generalizedBose-Hubbard-like Hamiltonians $\mathfrak{H}(\lambda)=H(v,v,0)+\lambda\,{\calV}$ for which the unitarity of the perturbed system is required. This leads tothe construction of two different families of Hamiltonians$\mathfrak{H}(\lambda)$. In the first one the number $N$ of bosons is assumedconserved while in the second family such an assumption is relaxed. In bothcases the anisotropy of the related physical Hilbert space is shown reflectedby a highly counterintuitive but operationally realizable structure ofadmissible perturbations $\lambda\,{\cal V}$.

Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation