Robe,
The 9mm is going to need additional parts, like 12lbs recoil spring, new fitted extractor, modified ejector to function reliably in your properly built 9x23.
Now, you can fit one gun for all three but it may not function reliably with the 9x23 ammo, I have witnessed this with the Colt Series 80 guns that were offered as a three barreled set in 9mm, .38Super, and 9x23.
The 9mm is a removed cousin of the 9x23 by a few generations and it will not provide the same shooting experience and recoil impulse/feel.
As an alternative, I would reccomend that you use .38 Super ammo for practice as it is widely available and fairly inexpensive.