Curious wrote:
"Will the output of two amplifiers add together in directions where the
signal is in phase, or will it act like two different signals and
therefore interfere with each other?"

For stereo?

The signals are coherent from two amplifiers or from one.

Two close antennas fed the same signal in the same phase generally add
broadside to the plane containing the antennas and cancel at right
angles to the lobes containing the added signals.

See page 91 of Kraus` 3rd efition of "Antennas" for: "Two Isotropic
Point Sources of the Same Amplitude and Phase."

Another example is the pair af CB antennas used by truckers, one on
either side of the truck cab, to reinforce the signal fore and aft of
the truck.

The 1/2-wave dipole is another example. Its two elements have the same
cuerrent amplitude and direction. Its lobes are broadside and its nulls
are at right angles off the tips of the elements.

Best regards, Richard Harrison, KB5WZI