Following the first observation of an astrophysical high-energy neutrino flux with the IceCube Neutrino Observatory in 2013 and the identification of a first cosmic high-energy neutrino source in 2017, the detector will be upgraded with about 700 new advanced optical sensors. This will expand IceCube's capabilities both at low and high neutrino energies. A large fraction of the upgrade modules will be multi-PMT Digital Optical Modules, mDOMs, each featuring 24 three-inch class photomultiplier tubes (PMTs) pointing uniformly in all directions, thereby providing an almost homogeneous angular coverage. The signal from each PMT is digitized individually, providing directional information for the incident photons. Together, the 24 PMTs provide an effective photosensitive area more than twice than that of the current IceCube optical module. The main mDOM design challenges arise from the constraints on the module size and power needed for the 24-channel high-voltage and readout systems. This contribution presents an mDOM design that meets these challenges and discusses the sensitivities expected from these modules.