One further requirement is that the base drive is high enough to make the amplifier stage be in class C at all Vcc values.
Varying Vcc varies the output power. The Vcc is the sum of a DC term for the carrier and an AC term for the audio making the modulation sidebands.
In the old days this was done with a transformer. The AC was put to the primary and the secondary was in series with the DC and the valve/tube being modulated.
There were alternate ways of doing this. Amateurs would sometimes modulate a 1W transmitter by absorbing the power to the antenna. A carbon microphone was put in series with the antenna transmission line.