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The paper presents a modified Constant Envelope Multiplexing with Intermodulation Construction (CEMIC) technique for multiplexing signals within a single frequency band. A constant envelope signal is necessary to operate a transponder at maximum efficiency. This paper proposes a novel scheme to incorporate backwards compatibility constraints into the cost function of the existing CEMIC scheme to minimize changes in the onboard navigation system and ground receivers. The proposed scheme maximizes multiplexing efficiency by optimizing signal power sharing as per system requirements. Simulation results indicate that the proposed scheme provides 0.1% to 13.7% better efficiency than the existing CEMIC scheme, depending upon the case severity. Furthermore, the power distribution and phasing of the individual intermodulation constituent signals are optimized to minimize intra-system and inter-system interference. As a result, the proposed scheme facilitates frequency coordination with GNSS service providers. The paper also discusses the hardware performance of the proposed scheme's composite signal.