Weird question re: balanced connection

Most likely yes.
My Audio Research Sp-15 has 'balanced out' and since it has them, it also has a pair of plus, and a pair off minus outputs in RCA next to the balanced jacks.
I do not know if it is for certain OK to split them in YOUR preamp. as the circuit may be different.
And as mentioned the second output is in negative phase. So you would reverse the leads on that amp to the speaker to keep it in phase.

You have to be careful since you will get bridged outputs if amplifiers have single ended (ground referenced) output. Bridged outputs will get you 4x power (while two power supplies are designed only for 2x more power total) plus doubled output impedance (affecting speaker damping), not to mention being not able to drive your speaker's properly if half of their minimum impedance (for the same current since voltage is 2x) is below amplifier's ability. If amp has already bridged outputs then the only improvement will be keeping system balanced. Fully differential output will cancel even order harmonics but I wouldn't bother since your beef is with increased odd order harmonics. Both amps have to have exactly same gain and phase shift or common mode reduction will be reduced. Doing thing like that is always risky proposition. Most likely you'll get better results selling all four monos and buying two better amps.

Thank you all for your responses.
Kijanki, that's exatly what I needed to know, thank you.

I second Kijanki’s good comments, and I would add that in addition to the possibility of over-stressing the amps due to the halved impedance each of them would see, I’m not even sure that you could turn the amps on and off without creating at least a small risk of damage.

As you are probably aware, running a tube amp that has an output transformer unloaded is not a healthy idea, especially if a signal is being put into it, but conceivably also during the startup and shutdown processes even if no signal is present. Transients that may occur in the amplifier circuitry at those times might in effect create a brief “signal.” And in the configuration you are proposing whichever amplifier in each channel pair is turned on first or off last would in effect be running unloaded for at least a brief amount of time.

Also, although this amp is not bridged (it uses two 845 tubes in a parallel SET configuration), I’ll mention that combining two bridged amps into a balanced pair configuration would be a sure invitation to damage. Combining two amps into a balanced pair configuration requires connecting one output terminal of one amp to one output terminal of the other amp (with those terminals not being connected to the speaker). With amps having single-ended outputs it would be the common or ground terminals that are connected together. But with bridged amps the result would be that output signals which are inverted relative to each other would be shorted together. Definitely not healthy!

Regards,
-- Al

Al, I did not realize it is a tube amp - thank you for clarifying it. I absolutely agree that it is very dangerous to play any games.

Cptaz, Follow Al's advise and don't do it!