Recently, hybrid non-orthogonal multiple access (H-NOMA) technology, which effectively utilizes both NOMA and orthogonal multiple access (OMA) technologies through flexible resource allocation in a single transmission, has demonstrated immense potential for enhancing the performance of wireless communication systems. To further release the potential of HNOMA, this paper proposes a novel design of H-NOMA which jointly incorporates hybrid successive interference cancellation (HSIC) and power adaptation (PA) in the NOMA transmission phase. To reveal the potential of the proposed HSIC-PA aided H-NOMA scheme, closed-form expression for the probability of the event that H-NOMA can achieve a higher data rate than pure OMA by consuming less energy is rigorously derived. Furthermore, the asymptotic analysis demonstrates that the probability of the proposed H-NOMA scheme approaches 1 in the high signal-to-noise ratio (SNR) regime without any constraints on either users' target rates or transmit power ratios. This represents a significant improvement over conventional H-NOMA schemes, which require specific restrictive conditions to achieve probability 1 at high SNRs as shown in existing work. The above observation indicates that with less energy consumption, the proposed HSIC-PA aided H-NOMA can achieve a higher data rate than pure OMA with probability 1 at high SNRs, and hence a higher energy efficiency. Finally, numerical results are provided to verify the accuracy of the analysis and also demonstrate the superior performance of the proposed H-NOMA scheme.