Abstract: Detection of high-energy neutrinos from distant astrophysical sources will open a new window on the Universe. The detection principle exploits the measurement of Cherenkov light emitted by charged particles resulting from neutrino interactions in the matter containing the telescope. A novel multi-PMT digital optical module (DOM) was developed to contain 31 3-inch photomultiplier tubes (PMTs). In order to maximize the detector sensitivity, each PMT will be surrounded by an expansion cone which collects photons that would otherwise miss the photocathode. Results for various angles of incidence with respect to the PMT surface indicate an increase in collection efficiency by 30% on average for angles up to 45 degrees with respect to the perpendicular. Ray-tracing calculations could reproduce the measurements, allowing to estimate an increase in the overall photocathode sensitivity, integrated over all angles of incidence, by 27% (for a single PMT). Prototype DOMs, being built by the KM3NeT consortium, will be equipped with these expansion cones.