Don't want to get pedantic with a noob Beth' but there is no such thing as a "stereo" XLR (tho' of course you could kludge one to take 2 channels) so let us stick with TRS?
The simplest way to get a "transparent" feed to two or more pieces of gear is a simple passive splitter.
"Sigh" It is SO sad and frustrating that people have largely lost/never learned some basic engineering and soldering skill. Making such a 3 way splitter* really is child's play, 4 TRS jack, some wire and a tin. Fitting switches is not very much more difficult.
In the absence of such skills you are looking at headphone amps with 4 outputs but these will not give you absolutely clean repro'. I doubt the good ones will add anything you can REALLY hear but you might not be 100% happy?
Then there are passive Monitor Controllers. These are essentially passive splitters with a VC pot and often a headphone amplifier (that needs power of course!)
*NB It is always ok to SPLIT outputs but not to COMBINE them. This can lead to distortion as one low Z output is loaded by another. In some cases with older gear you can even damage the OP amplifiers. Combiners need build out resistors, usually around 1k per "leg" .
BTW I can do diagrams if you want to have a bash?
Dave.