Most places nowadays have limits on loudness as it is actually quite easy to go above unsafe limits, and various countries in turn have placed limits on things (originally mostly France but that spread to Europe and nobody wants to make Europe only models, and also then risk a lawsuit in a few years in the US when someone tries something on then). Most then go find old school stuff that was around before the various limitations were put in.
Depending upon how soldering iron happy you are there might be options for both adding bluetooth (simple battery powered things exist and over the ear cans tend to have a lot of space in the back) and possibly increasing loudness*.
*normally loudness limitations are provided by a resistor -- if you have a minimum resistance at all times then it is never going to go above a certain loudness. Replace this with a lower rated resistor and you have more to go to the sound rather than being burned off as heat from the resistor. Some also note things like the sound levels being set by a reference resistor inside your device (the regs also tended to apply here) and thus can be changed by changing that
https://gbatemp.net/threads/hardwar...volume-of-your-3ds-some-models-so-far.400221/ for a popular example of such things.
You will tend to want low impedance headphones or indeed low impedance components thereof to go with it -- no point in having a superconductor leading up to the coil if the coil was never going to pass enough power to get loud anyway. This can be selected for a bit but you are going to have to go looking.
I will also note most don't necessarily want loudness as much as the ability to drown out outside sounds. In that case might be worth looking into some of the active noise cancellation setups, though budget tends to be an issue there as most such things (especially good ones) tend to be pricier owing to being more than a speaker coil and a bit of wire like open backed or passive noise cancellation options (bit of foam and a good seal around the ear).
I am not a great fan of noise cancellation -- makes me want to fall over, sometimes even more than in ear ones do, so if you can try such a thing then do so.
