If your Bluetooth headphone has a 3.5 mm audio jack, XPUMP should work well.
Otherwise, you will need to add an extra Bluetooth transmitter to pair with it.
Bluetooth speakers such as Bose Soundlink mini and Jambox all work well with XPUMP as both of them have the most common 3.5 mm audio input.
We have tried XPUMP with some popular speakers such as: Audio Engine A2, Bose soundlink mini, Jawbone Jambox, FOSTEX PM0.3, Altec Lansing VS3020/ VS2720, Edifier Luna Eclipse and harman/kardon SoundSticks III 2.1.
They all work together very well and match well with each other. XPUMP also works well with PS4 if you just add an optical-to-analog converter.
We also think XPUMP can also work with your 5.1/7.1 sound system although you might already be very satisfied with your original setting. As for headphones, we think theoretically any wired headphone can work with XPUMP.
Please let us know what kind of stereo speakers, sound bars or headphones you want to match XPUMP with. And our engineering team would get back to you very soon.