  We study multi-soliton solutions of the four-dimensional SU(N) Skyrme model
by combining the hedgehog ansatz for SU(N) based on the harmonic maps of
$S^{2}$ into $CP^{N-1}$ and a geometrical trick which allows to analyze
explicitly finite-volume effects without breaking the relevant symmetries of
the ansatz. The geometric setup allows to introduce a parameter which is
related to the 't Hooft coupling of a suitable large $N$ limit, in which
$N\rightarrow\infty$ and the curvature of the background metric approaches
zero, in such a way that their product is constant. The relevance of such a
parameter to the physics of the system is pointed out. In particular, we
discuss how the discrete symmetries of the configurations depend on it.
