a common stock level accross all variations

There is a workaround for this. You will need to write a small module for this.

In a proper stock event hook - before the stock event is executed - just set stock to the minimum of any other product variation.
You may want also to copy stock level back to those other variations as well.

The only drawback - is when you actually want to increase stock you will have to do it for all of the variations at the same time.
But here you can detect what is the source of changing the stock levels and in the same module you could do an exception - and in that case just duplicate transaction to every other variation.