Connecting multipe amps to a single DAC

[the machine]

Hello All,

Looking for some recommendations here, as I'm assuming there is a product that can do this, but I'm not sure exactly what I'm looking for.

I have 4 headphone amps that I'm not willing to part with, and one DAC. Is there an RCA input switch that I can use that will allow me to plug all the amps into the DAC and just click a button or switch to toggle between amps? Also, one of the amps will use balanced and I'm unsure if having all of these plugged into the DAC at one time will work properly.

Just to line it all up

Amps:
THX 789 AAA
Audeze Deckard
Beyerdynamic A2
Woo Audio WA7

DAC:
Topping D70

So I want to run the balanced connections for the 789, then plug the other three into any RCA switch or port or whatever then click a button to use either RCA 1 2 or 3. I'm also not sure if this would work, having an amp plugged in via balanced connections and one plugged in via RCA. Not sure how the DAC would know where to send the signal (my knowledge of electrical engineering is nil, so forgive the ignorance if what I'm saying makes little to no sense)

Thanks

 

[Speedskater]

There are (or were) many such passive RCA units, I have an old Radio Shack unit.
But trying to do both RCA and XLR outputs gets real tricky real fast. Probably a power semi-pro unit would be best.

 

[the machine]

Thanks, can you provide any examples to what you're referring to? I could always just unplug the RCA jack from the DAC when using the 789 and vice versa. Just don't want to have to switch between 3 different RCA's when I feel like using something different.