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By using the known operator product expansions (OPEs) between the lowest $16$higher spin currents of spins $(1, \frac{3}{2}, \frac{3}{2}, \frac{3}{2},\frac{3}{2}, 2,2,2,2,2,2, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2},3)$ in an extension of the large ${\cal N}=4$ linear superconformal algebra,one determines the OPEs between the lowest $16$ higher spin currents in anextension of the large ${\cal N}=4$ nonlinear superconformal algebra forgeneric $N$ and $k$. The Wolf space coset contains the group $G =SU(N+2)$ andthe affine Kac-Moody spin $1$ current has the level $k$. The next $16$ higherspin currents of spins $(2,\frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2},3,3,3,3,3,3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2},4)$ arise inthe above OPEs. The most general lowest higher spin $2$ current in thismultiplet can be determined in terms of affine Kac-Moody spin $\frac{1}{2}, 1$currents. By careful analysis of the zero mode (higher spin) eigenvalueequations, the three-point functions of bosonic higher spin $2, 3, 4$ currentswith two scalars are obtained for finite $N$ and $k$. Furthermore, we alsoanalyze the three-point functions of bosonic higher spin $2, 3, 4$ currents inthe extension of the large ${\cal N}=4$ linear superconformal algebra. It turnsout that the three-point functions of higher spin $2,3$ currents in the twocases are equal to each other at finite $N$ and $k$. Under the large $(N,k)$ 'tHooft limit, the two descriptions for the three-point functions of higher spin$4$ current coincide with each other. The higher spin extension of $SO(4)$Knizhnik Bershadsky algebra is described.

The Next $16$ Higher Spin Currents and Three-Point Functions in the Large ${\cal N}=4$ Holography