The regenerative capabilities of next-generation satellite systems offer a novel approach to design low earth orbit (LEO) satellite communication systems, enabling full flexibility in bandwidth and spot beam management, power control, and onboard data processing. These advancements allow the implementation of intelligent spatial multiplexing techniques, addressing the ever-increasing demand for future broadband data traffic. Existing satellite resource management solutions, however, do not fully exploit these capabilities. To address this issue, a novel framework called flexible resource management algorithm for LEO satellites (FLARE-LEO) is proposed to jointly design bandwidth, power, and spot beam coverage optimized for the geographic distribution of users. It incorporates multispot beam multicasting, spatial multiplexing, caching, and handover (HO). In particular, the spot beam coverage is optimized by using the unsupervised K-means algorithm applied to the realistic geographical user demands, followed by a proposed successive convex approximation (SCA)-based iterative algorithm for optimizing the radio resources. Furthermore, we propose two joint transmission architectures during the HO period, which jointly estimate the downlink channel state information (CSI) using deep learning and optimize the transmit power of the LEOs involved in the HO process to improve the overall system throughput. Simulations demonstrate superior performance in terms of delivery time reduction of the proposed algorithm over the existing solutions.