Alternative Binary Offset Carrier (AltBOC) modulation signal has the constraint of an equal power allocation scheme. Thus, it is not flexible enough to meet different requirements. To solve this problem, we propose a General AltBOC (GAltBOC) modulation. The proposed technique can achieve the same function as AltBOC. Meanwhile, its power allocation ratio can be adjusted when required. The detailed derivation of the GAltBOC modulation is presented, and three representative cases as well as the signal properties are discussed. To further improve the combination efficiency, we develop the Interlacing GAltBOC (IGAltBOC) modulation based on the GAltBOC modulation. The Power Spectrum Density (PSD) and correlation functions of the proposed signals are verified by simulation. The code tracking error and implementation complexities are analysed and compared with existing methods. Results show the proposed signals indeed enhance the flexibility of power allocation ratio with the same level code tracking accuracy. Compared with AltBOC modulation, the proposed signal can reach a higher combination efficiency at the expense of relatively higher implementation complexity. Compared with Asymmetric Constant Envelope Double-sideband (ACED) modulation, the proposed signals have significantly lower complexity of signal generation, which is helpful in simplifying the signal generation in the payload transmitter.