Unusual modulation

I've been writing a SciFi story, and it calls for something very unusual to happen. I'd like to check this idea for plausibility, but as I'm not a radio ham myself, I don't know if this already exists (and if so under what name) or if it is totally impossible.

If I have a normal modulated radio signal that can, if broadcast, be picked up by a normal radio receiver — purely for example, let's say it's the normal broadcast from a typical 25 MHz AM radio station — can I use that modulated radio signal to itself modulate a much higher frequency carrier wave in such a way that the radio station's signal will come out of the speakers of a totally unmodified radio tuned to 25 MHz?

This is an illustration of my intention, where y_1 is the signal, y_2 is the signal modulated by the first carrier wave, and y_3 is y_2 modulated by the next carrier wave. (I chose the constants here purely for the visuals, don't take them to mean anything precise). To rephrase the question: Can y_1 come out of the speakers if y_3 is what's hitting the antenna, and the circuit was tuned for y_2?

The intention here is to cheat the normal rules about gain, given the transmitter is a fixed size and power and the receiver is a fixed size and frequency, and nobody was expecting them to be so far apart.

I'm still interested if the answer is in the form of "yes, but" for example "yes, but that won't ever work for FM" or "yes, but there is an extra restriction on the frequencies, which is…"

• Possibly of interest: ham.stackexchange.com/questions/13257/… Jul 26, 2019 at 16:08
• Excellent, thank you. I couldn't search for that myself, because I wasn't aware it might be called "nested" or "double" modulation. Jul 27, 2019 at 11:23