  The high energy photoproduction of jets is being observed at the ep collider,
HERA. It may be that the HERA centre-of-mass energy is sufficiently large that
the production of more than one pair of jets per ep collision becomes possible,
owing to the large number density of the probed gluons. We construct a Monte
Carlo model of such multiparton interactions and study their effects on a wide
range of physical observables. The conclusion is that multiple interactions
could have very significant effects upon the photoproduction final state and
that this would for example make extractions of the gluon density in the photon
rather difficult. Total rates for the production of many (i.e. > 2) jets could
provide direct evidence for the presence of multiple interactions, although
parton showering and hadronization significantly affect low transverse energy
jets.
