  We consider a mesoscopic superconducting island hosting multiple pairs of
Majorana zero-energy modes. The Majorana island consists of multiple p-wave
wires connected together by a trivial (s-wave) superconducting backbone and is
characterized by an overall charging energy $E_C$; the wires are coupled to
normal-metal leads via tunnel junctions. We calculate the average charge on the
island as well as non-local conductance matrix as a function of a p-wave
pairing gap $\Delta_P$, charging energy $E_C$ and dimensionless junction
conductances $g_i$. We find that the presence of a topological ground-state
degeneracy in the island dramatically enhances charge fluctuations and leads to
the suppression of Coulomb blockade effects. In contrast with conventional
(s-wave) mesoscopic superconducting islands, we find that Coulomb blockade
oscillations of conductance are suppressed in Majorana islands regardless of
the ratio $E_C/\Delta_P$ or the magnitude of the conductances $g_i$. We also
discuss our findings in relation to the so-called topological Kondo effect.
