In the paper herein we treat some problems concerning the metric structure on the 2-tangent bundle: $T^2M$. We determine the set of all metric semi-symmetric $N$-linear connections, in the case when the nonlinear connection $N$ is fixed. We prove that the sets: $\mathcal T_N$ of the transformations of $N$-linear connection having the same nonlinear connections $N$ and $\overset{ms}{\mathcal T}_N$ of the transformations of metric semi-symmetric $N$-linear connections, having the same nonlinear connection $N$, together with the composition of mappings are groups. We obtain some important invariants of the group $\overset{ms}{\mathcal T}_N$ and we give their properties. We also study the transformation laws of the torsion and curvature $d$-tensor fields, with respect to the transformations of the groups $\mathcal T_N$ and $\overset{ms}{\mathcal T}_N$.