Three main changes are currently taking place in the context of the automotive industry: electrification of vehicle propulsion, automated driving and a shift towards mobility as a service. While the first two represent opportunities for the industry growth, the later questions the private ownership of a car. Keeping the concept of a privately owned car will involve reducing the economical and environmental cost of such ownership. In this paper, we address the reduction of the parking footprint of cars, leveraging on electrification and low-level driving automation to more than double the density of cars parked in a given area, compared to conventional parking lots. We perform a complete evaluation of different strategies of vehicle coordination based on large-scale datasets of parking sessions in distinct scenarios and under varying demand patterns. Our results on the key metrics, namely area per vehicle, travel distance while parked, and removal time - clearly highlight the relevance and efficiency of this novel approach to parking. We also empirically derive guidelines for designing high-density parking systems (e.g. parking lot layout or capacity) and show the involved trade-offs.