The era of the fifth-generation (5G) New Radio (NR) technology has just begun, and its promises to substantially improve the system performance have turned into reality. The 5G NR enabled Non-Terrestrial Network (NTN) is almost upon us and will represent an effective solution to provide services anytime, anywhere, and over wider coverage areas. In this context, high throughput satellite systems with advanced multi-beam transmissions have gained significant attention owing to their ability to boost the system capacity through beam frequency re-use, increased user data rates, and system spectral efficiency. In this paper, we propose a novel radio resource management scheme, named Single-Frequency Multi-Beam Transmission (SF-MBT), for efficient delivery of the enhanced Mobile Broadband (eMBB) services over the 5G NR multi-beam NTN systems. The main thinking is to group beams into the dedicated Beam Areas, wherein a certain content flow is delivered via simultaneous multi-beam transmissions over the same radio resources without causing inter-beam interference. A simulation campaign is conducted under different scenarios to assess the effectiveness of the proposed SF-MBT algorithm as compared to the current schemes based on frequency reuse. System-wide performance is evaluated in terms of the aggregate data rate, mean throughput, and system spectral efficiency.