Membrane proteins can deform the lipid bilayer in which they are embedded. If the bilayer is treated as an elastic medium, then these deformations will generate elastic interactions between the proteins. The interaction between a single pair is repulsive. However, for three or more proteins, we show that there are nonpairwise forces whose magnitude is similar to the pairwise forces. When there are five or more proteins, we show that the nonpairwise forces permit the existence of stable protein aggregates, despite their pairwise repulsions.