The high energy photoproduction of jets is being observed at the ep co
llider, HERA. It may be that the HERA centre-of-mass energy is suffici
ently large that the production of more than one pair of jets per ep c
ollision becomes possible, owing to the large number density of the pr
obed gluons. We construct a Monte Carlo model of such multiparton inte
ractions and study their effects on a wide range of physical observabl
es. The conclusion is that multiple interactions could have very signi
ficant effects upon the photoproduction final state and that this woul
d for example make extractions of the gluon density in the photon rath
er difficult. Total rates for the production of many (i.e. greater tha
n or equal to 3) jets could provide direct evidence for the presence o
f multiple interactions, although parton showering and hadronization s
ignificantly affect low transverse energy jets.