Progressing cavity pumps. The rotor executes a rolling motion in the stator, because of the different auger like shapes of rotor and stator the cavity between moves along the axis. This video shows the movement.
Rolling diphragms have been around for many years now. See...
With or without the spring.
(With enough vacuum in the top you can get the membrane to slip upwards, but it is easily reset by cycling.)
Fabric reinforcement helps prevent stretch, but generally everything is elastic to some extent.
The bigger pump affects the smaller pump by changing the system when it is on.
In this case, the bigger pump will cause the pressure at the inlet to the smaller pump to drop. The pressure drop will be proportional to the inlet pipe run. This pressure drop would reduce flow through the small pump.
One could imagine a scenario where a large pump causes ...