Investigating innovative satellite architectures with enhanced system through- put is one of the most important challenges towards realizing the next generation of satellite communication systems. In this context, we study two advanced architectures, namely cooperative and cognitive satellite systems. These designs allow the spectral coexistence of two multibeam satellites over a common coverage area with the overlapping beam patterns. In the cooperative dual satellite system, we consider coordination between two coexisting transmitters in order to reduce the intersatellite interference. This is achieved by employing adequate user scheduling, based on the channel state information of each user. To this end, a semi-orthogonal interference aware scheduling algorithm is applied. Further, in the cognitive dual satellite system, we employ a cognitive beamhopping technique assuming that the secondary gateway is aware of the primary's beamhopping pattern. Moreover, we compare the performances of these schemes with those of the conventional multi- beam and overlapping dual satellite systems in terms of spectral efficiency, power efficiency and user fairness. Finally, we provide several insights on the performance of these schemes and provide interesting future works in these domains.