  We prove an upper bound of higher topological complexity $TC_n(X)$ using
higher $\mathcal{D}$-topological complexity $TC_n^{\mathcal{D}}(X)$ of a space
$X$. An intermediate invariant $\widetilde{TC}_n(X)$ is used in the proof. We
interpret this invariant $\widetilde{TC}_n(X)$ as higher analogue of strongly
equivariant topological complexity of the universal cover of $\widetilde{X}$
with the action of the fundamental group of $X$.
