We investigate the multiplicity of extragalactic sources detected by the Herschel Space Observatory in the COSMOS field. Using 3.6- and 24-$mu$m catalogues, in conjunction with 250-$mu$m data from Herschel, we seek to determine if a significant fraction of Herschel sources are composed of multiple components emitting at 250 $mu$m. We use the XID+ code, using Bayesian inference methods to produce probability distributions of the possible contributions to the observed 250-$mu$m flux for each potential component. The fraction of Herschel flux assigned to the brightest component is highest for sources with total 250-$mu$m fluxes < 45 mJy; however, the flux in the brightest component is still highest in the brightest Herschel sources. The faintest 250-$mu$m sources (30-45 mJy) have the majority of their flux assigned to a single bright component; the second brightest component is typically significantly weaker, and contains the remainder of the 250-$mu$m source flux. At the highest 250-$mu$m fluxes (45-110 mJy), the brightest and second brightest components are assigned roughly equal fluxes, and together are insufficient to reach 100 per cent of the 250-$mu$m source flux. This indicates that additional components are required, beyond the brightest two components, to reproduce the observed flux. 95 per cent of the sources in our sample have a second component that contains more than 10 per cent of the total source flux. Particularly for the brightest Herschel sources, assigning the total flux to a single source may overestimate the flux contributed by around 150 per cent.
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