Just as push-pull operation doubled the single-ended solo output tube, mixed class operation doubles push-pull's double output tubes; thus at least four output tubes are needed. One pair runs in Class-A push-pull and the second pair runs in Class-AB or Class-B (or even Class-C) push-pull. Thus, the first pair are always conducting, while the second pair can be completely turned off (or run at a much lower current) at idle.
As the signal level increases, the second pair is activated, unburdening the first pair and greatly increasing the output power. In fact, we can just as easily mix Class-AB with Class-B or Class-C, either mix would give even greater power output.
In fact, we could easily create a three-way mix of operating classes, say Class-A, Class-AB, and Class-B, or Class-AB, Class-B, and Class-C. Of course, at least six output tubes would be needed. In all the mixes, the goal would be the same: to create a simple, seamless sounding push-pull amplifier that uses only a single input and phase splitting (and driver) stage per amplifier. This goal can met with an near infinite mix of output tube types and bias points. One example is using a pair of EL34s for the Class-A grouping and KT88s for the Class-B pairing. Another example might be using a pair of 300Bs for the Class-AB grouping and 211s for the Class-C pairing.
How to proceed?
Two separate amplifiers on two separate chassis with two separate power supplies could be used; but what a hassle. Using one chassis with one power supply and one input stage is preferable.