Sure, this is not only possible, but even has some advantages over single-plane propellers. The catch is you ideally want the two to spin in opposite directions to cancel out torque and vibration.
You're building a contra-rotating propeller:
Pictured is a Sun Flightcraft contra-rotating gearbox kit for Rotax 503 and Rotax 582 engines.
Although more efficient (on the order of 10%) than single-plane propellers, they are also much more complicated to design. The gearbox will be heavier and harder to maintain. And they are also often much louder, although the Rotax kit pictured above is claimed to be quieter.
They're not just for small engines. Here's a Tu-95 strategic bomber:
On helicopters, the same idea is called coaxial rotors:
"Co-rotating" propellers are also possible, but far less common, as the key advantages (efficiency and cancellation of torque and vibration) are reduced or lost. I could only find some academic papers on it. Here is another.