Erik, are you sure about that? From the manual for the A23:
The Input Stage:
Also, while grounding pin 3 of an XLR input connector (the inverted signal pin) would be appropriate in many cases if that input were driven by a balanced output that is transformer coupled, or is actively driven but is "floating" with respect to ground, it could potentially cause performance problems, or conceivably even damage over the long-term, to some components having actively driven balanced outputs. (See this thread for an example of a CD player that buzzed as a result of pin 3 being grounded by an adapter cable). Yet the manual for the A23 provides no cautions about the potential for any such issues.
A component can have input and/or output circuits that are balanced and differential regardless of whether the rest of its internal signal path is balanced and differential or not. If the entire signal path of a component is balanced, it is usually referred to as being “fully balanced,” or words to that effect.
In this case I’m pretty certain that aside from its input circuits the internal signal path of the A21 is single-ended, but several things in its description, specs, and manual appear to indicate that its input circuits which receive the signals provided to its XLR connectors are in fact balanced and differential. Including a statement in its description that it provides "balanced inputs with discrete circuits and XLR connectors"; the fact that its input impedance is specified as "33 k Ω unbalanced; 66 k Ω balanced"; and various statements in the manual referring to the advantages of balanced interconnections.
Also, while it is true that connecting a balanced output to a balanced input (as you indicated you would be doing in connecting the Mytek DAC to the A21) will often result in 6 db more overall system gain than would be provided by an unbalanced connection between the same components, that is not always the case. It depends on the designs of the specific interface circuits in **both** components. And after looking at the descriptions and manuals of the two components I don’t see enough information to determine the answer in this case.
BTW, I see also that the Brooklyn DAC incorporates internal jumpers that are said to provide the capability of reducing its output levels by 6 db. That may not have any relevance to your question, but I thought I’d point it out.
Are you sure you meant A24? I can’t find any reference to a Parasound A24 among both current and discontinued products that are listed at their website, or via a Google search.
Also, if you meant A23 (or various other Parasound amplifier models), as far as I can tell its XLR inputs are balanced, not unbalanced as you indicated above.
Finally, what model is the Mytek?