Iron grown on room-temperature CaF2/Si(111) substrates form two-dimensional arrays of nanometer-sized superparamagnetic islands. Deposition of Ag on the Fe/CaF2/Si(111) produced a superparamagnetic response where the effective moment was proportional to the number of Fe islands covered by an average-sized Ag island. The nonmagnetic Ag overlayer mediates a long-range exchange between neighboring Fe islands within an individual Ag island. Monte Carlo methods are used to examine ordering in two dimensions and to set minimum interisland coupling strengths.