Motivated by the intrinsic characteristics of mmWave technologies, we discuss the possibility of an authorization regime that allows spectrum sharing between multiple operators, also referred to as spectrum pooling. In particular, considering user rate as the performance measure, we assess the benefit of coordination among the networks of different operators, study the impact of beamforming both at the base stations and at the user terminals, and analyze the pooling performance at different frequency carriers. We also discuss the enabling spectrum mechanisms, architectures, and protocols required to make spectrum pooling work in real networks. Our initial results show that, from a technical perspective, spectrum pooling at mmWave has the potential for a more efficient spectrum use than a traditional exclusive spectrum allocation to a single operator. However, further studies are needed in order to reach a thorough understanding of this matter, and we hope that this paper will help stimulate further research in this area.