A significant feature of the modernised Global Navigation Satellite System (GNSS) signals is that there are multiple signal components needing to be transmitted on a carrier frequency. How to combine these signal components into a constant envelope composite signal is a challenge. Existing constant envelope modulation techniques have some limitations, and are not effective enough. To solve this problem, we propose a quasi-constant-envelope multiplexing technique in this paper. The proposed method is based on numerical optimisation, and can work in two ways. The corresponding objective functions are provided. To verify the performance of the proposed method, we present three application examples. Results show that the first variation of our method can reach the same combining performance as Phase-Optimised Constant-Envelope Transmission (POCET). In the second variation, the combining efficiency can be pre-set. We can reach higher combining efficiency than POCET, and the envelope of the composite signal becomes quasi-constant. Furthermore, the inter-modulation signals in the final composite signal are adjustable. With the help of the proposed method, we can learn more details of the combining scheme than with POCET.