What do you think is a carrier's maximum modulation index without over-modulation?

The maximum modulation index for a carrier signal without resulting in over-modulation typically depends on the modulation scheme being used. For standard amplitude modulation (AM), the maximum modulation index is generally 1, meaning the peak envelope power of the modulated signal should not exceed the carrier power. In frequency modulation (FM), the modulation index can be higher, but it should still be kept within limits defined by the system to avoid distortion. Ultimately, the precise value can vary based on specific application requirements and the desired quality of the transmitted signal.