  We study systems of multiple interacting quantum impurities deposited on a
metallic surface in a 3D host. For the real-space two-impurity problem, using
numerical renormalization group calculations, a rich range of behavior is shown
to arise due to the interplay between Kondo physics and effective RKKY
interactions - provided the impurity separation is small. Such calculations
allow identification of the minimum impurity separation required for a
description in terms of independent impurities, and thereby the onset of the
'dilute impurity limit' in many-impurity systems. A 'dilute cluster' limit is
also identified in systems with higher impurity density, where inter-impurity
interactions are only important within independent clusters. We calculate the
quasiparticle interference (QPI) due to two and many impurities, and explore
the consequences of the independent impurity/cluster paradigms. Our results
provide a framework to investigate the effects of disorder due to interacting
impurities at experimentally relevant surface coverages.
