The usable satellite spectrum is becoming scarce due to continuously increasing demand for broadcast and multimedia services. In this context, we consider the problem of enhancing spectral efficiency in multibeam satellite networks. The spectral coexistence scenario of two multibeam satellites over a common coverage area is studied with a primary satellite having larger beams and a secondary satellite having smaller beams. Furthermore, a novel cognitive beamhopping satellite system is proposed. The system performance of the proposed system is evaluated and compared with that of conventional multibeam and beamhopping systems in terms of system throughput. It is shown that the proposed system significantly enhances the spectral efficiency in comparison to other systems. Moreover, the scenario of the presence of multiple secondary users within an inactive primary beam is considered with power control on the secondary transmission. The system performance is evaluated by considering partial and full frequency sharing approaches. It is noted that the total spectral efficiency increases with the number of secondary users in the full frequency reuse approach.