In an open economy, outside money in positive supply does not eliminate the real indeterminacy which arises under uncertainty and incomplete asset markets. If money supply is subject to shocks or is not perfectly credible in all countries, the level of a fixed exchange rate matters. Analogous results obtain in cash-in-advance models.
Salto, M. (1998). Indeterminacy of equilibrium allocations in monetary open economies (CORE Discussion Papers 1998/62). https://hdl.handle.net/2078.5/35731