It was recently demonstrated that the $N=0,1,2,4$ super–Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite–dimensional (super)conformal groups $SL(2,R)$, $OSp\left(1\right|2)$, $SU(1,1|1)$, and $SU(1,1|2)$, respectively. In this work, a similar scheme is realised for $OSp\left(3\right|2)$. It is shown that the $N=3$ case exhibits a surprisingly richer structure of invariants, the $N=3$ super–Schwarzian being a particular member. We suggest that the extra invariants may prove useful in building an $N=3$ supersymmetric extension of the Sachdev–Ye–Kitaev model.