The interaction of multiple Coronal Mass Ejections (CMEs) has been observed
by LASCO coronagraphs and by near-Earth spacecraft, and it is thought to be an
important cause of geo-effective storms, large Solar Energetic Particles events
and intense Type II radio bursts. New and future missions such as STEREO, the
LWS Sentinels, and the Solar Orbiter will provide additional observations of
the interaction of multiple CMEs between the Sun and the Earth. We present the
results of simulations of two and more CMEs interacting in the inner
heliosphere performed with the Space Weather Modeling Framework (SWMF). Based
on those simulations, we discuss the observational evidence of the interaction
of multiple CMEs, both in situ and from coronagraphs. The clearest evidence of
the interaction of the CMEs are the large temperature in the sheath, due to the
shocks merging, and the brightness increase in coronagraphic images, associated
with the interaction of the leading edges. The importance of having multiple
satellites at different distances and angular positions from the Sun is also
discussed.