We analyze the mechanism of condensation of orientational moduli [as introduced in Phys. Rev. D 87, 025025 (2013)] on multi-Skyrmionic configurations of the four-dimensional Skyrme model. The present analysis reveals interesting novel features. First of all, the orientational moduli tend to decrease the repulsive interactions between Skyrmions, the effect decreasing with the increase of the baryon number. Moreover, in the case of a single Skyrmion, the appearance of moduli is energetically favorable if finite-volume effects are present. Otherwise, in the usual flat topologically trivial case, it is not. In the low-energy theory these solutions can be interpreted as Skyrmions with additional isospin degrees of freedom.