In the {{mathcal {N}}}=2 supersymmetric coset model, frac{SU(N+M)_k times SO(2 N M)_1}{ SU(N)_{k+M} times U(1)_{ N M (N+M)(k+N+M)}}, we construct the SU(M) nonsinglet {{mathcal {N}}}=2 multiplet of spins (1, frac{3}{2}, frac{3}{2}, 2) in terms of coset fields. The next SU(M) singlet and nonsinglet {{mathcal {N}}}=2 multiplets of spins (2, frac{5}{2}, frac{5}{2}, 3) are determined by applying the {{mathcal {N}}}=2 supersymmetry currents of spin frac{3}{2} to the bosonic singlet and nonsinglet currents of spin 3 in the bosonic coset model. We also obtain the operator product expansions (OPEs) between the currents of the {{mathcal {N}}}=2 superconformal algebra and above three kinds of {{mathcal {N}}}=2 multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of {{mathcal {N}}}=2 “rectangular W-algebra”, of the M times M matrix generalization of mathcal{N}=2AdS_3 higher spin theory in the bulk. The structure constants in the right hand sides of these OPEs are dependent on the three parameters k, N and M explicitly. Moreover, the OPEs between SU(M) nonsinglet {{mathcal {N}}}=2 multiplet of spins (1, frac{3}{2}, frac{3}{2}, 2) and itself are analyzed in detail. The complete OPE between the lowest component of the SU(M) singlet {{mathcal {N}}}=2 multiplet of spins (2, frac{5}{2}, frac{5}{2}, 3) and itself is described. In particular, when M=2, it is known that the above {{mathcal {N}}}=2 supersymmetric coset model provides the realization of the extension of the large {{mathcal {N}}}=4 nonlinear superconformal algebra. We determine the currents of the large {{mathcal {N}}}=4 nonlinear superconformal algebra and the higher spin-frac{3}{2}, 2 currents of the lowest {{mathcal {N}}}=4 multiplet for generic k and N in terms of the coset fields. For the remaining higher spin-frac{5}{2},3 currents of the lowest mathcal{N}=4 multiplet, some of the results are given.