Aside from multiple outputs from a CDP, doesn't your integrated amplifier/preamplifier have a tape loop? That's basically just the input connected to an output jack. Other amplifiers have either a tape loop, or as is more common, a preamp output, so using a dedicated power amp, or if your integrated amp has a power amp-preamp bypass input, would be an option.
Also, multiple outputs on the same CDPs are usually not the same kind of output. Back when many CDPs had their own headphone drivers (and the amps didn't) one RCA pair was a preamp output controlled by the potentiometer on the headphone amp. Nowadays one set might be Balanced XLR, or as in tube CDPs, a solid state output that either bypasses the tube stage (in which case the tubes really just add color after the chip analog output stage, usually op-amps as rollable as the tubes), or it really has an option between two output stages. I've seen a few that have all three but can't recall what brands, and as far as I remember from users, they mostly use the SS output for when they haven't replaced broken tubes yet; XLRs almost never, but that's with speaker set-ups. Given you can probably find a headphone amp with XLR inputs at a lower price than balanced speaker amps, one with deep pockets could conceivably use such a player on a speaker system then hook up something like a Mjolnir via XLR for when headphones would be more appropriate, like late at night.
