  We employ the intertwining operator technique to synthesize a supersymmetric
(SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent
to a spin-$(N-1)/2$ under an effective magnetic field. By considering an
additional imaginary magnetic field, we obtain a generalized
parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of
coupled resonators or waveguides under a gradient gain and loss; all the $N$
energy levels coalesce at an exceptional point (EP), forming the isotropic
high-order EP with $N$ states coalescence (EPN). Near the EPN, the scaling
exponent of phase rigidity for each eigenstate is $(N-1)/2$; the eigen
frequency response to the perturbation $\epsilon$ acting on the resonator or
waveguide couplings is $\epsilon^{1/N}$. Our findings reveal the importance of
the intertwining operator technique for the spectral engineering and exemplify
the practical application in non-Hermitian physics.
