We are going to use a horn to maximize the sound created by a vibrating diaphragm, as in a horn loudspeaker.
When the voltage applied to the vibrating diaphragm is kept constant, is there a limit to the additional sound pressure level that the horn can amplify?
A horn does two things: it creates directivity and it's also an impedance transformer, i.e. it gets the radiation impedance of the driver closer to the free field impedance of air.
The directivity gain is simply a function of geometry: the narrower the beam, the higher the sound pressure will be. At some you will run into practical limits: the narrower the beam and the lower the frequency, the larger the horn will need to be.
The impedance transformation is more complicated and depends a lot on the specifics of the driver and the specific geometry of the horn. You are still limited by conservation of energy, i.e. the acoustic energy cannot exceed the electrical energy you put in. For a perfect impedance match, you will get about 50% efficiency, but that's a lofty goal.
