  In this paper, we initiate the study of the global stability of nonlinear
wave equations with initial data that are not required to be localized around a
single point. More precisely, we allow small initial data localized around any
finite collection of points which can be arbitrarily far from one another.
Existing techniques do not directly apply to this setting because they require
norms with radial weights away from some center to be small. The smallness we
require on the data is measured in a norm which does not depend on the scale of
the configuration of the data.
  Our method of proof relies on a close analysis of the geometry of the
interaction between waves originating from different sources. We prove
estimates on the bilinear forms encoding the interaction, which allow us to
show improved bounds for the energy of the solution. We finally apply a variant
of the vector field method involving modified Klainerman--Sobolev estimates to
prove global stability. As a corollary of our proof, we are able to show global
existence for a class of data whose $H^1$ norm is arbitrarily large.
