An $n$-quasigroup is completely reducible if it can be represented by $n-1$ binary quasigroups. In this paper complete reducibility of totally symmetric (TS) $n$-quasigroups and $n$-loops was considered, $n\geq 3$. It is proved that for every completely reducible TS $n$-quasigroup $(Q,f)$, there exist an abelian group $(Q,+)$, a permutation $\varphi$ of $Q$ and $b\in Q$ such that for all $x^n_1\in Qf(x^n_1)=\varphi^{-1}(\sum^n_{i=1}\varphi x_i+b)$. It is also proved that every TS $n$-loop $(Q,f)$, is an $n$-group with unit iff $(Q^1,f)$ is completely reducible (in [3] an incorrect proof of this theorem was given). There exists a completely reducible TS $n$-loop of order $q$ iff $q=2^k$, $k\in N$. A corollary of this is that for every $q\equiv 2,4(\mod 6)$, $q\neq2^k$, there exists a TS 3-loop of order $q$ which is not completely reducible.