the real fix is to have a source with incredibly low background noise, or to avoid overly sensitive IEMs. nobody is ever happy about such an alternative.
for a DAP, you can replace it or add an amplifier that's known to have low background noise and handle low impedance IEMs fine(which is NOT what most portable amps are designed for!). another option is to add one of those fancy voltage divider cables(ifi audio sells some of those. Earbuddy or some name like that), you basically attenuate everything, music and noise, then hopefully when you increase the volume of the DAP to compensate for that wasted power, the background noise remains low. it works very well most of the time, but there are 2 things to consider:
1/ you need to have ample voltage headroom in your DAP to compensate for the attenuation and still reach the loudness you want.
2/ the extra circuit will affect the impedance "perceived" by the amp, and also by the IEM. that could result in audible change in signature, and in case of a low impedance IEM, it could also end up limiting the current(which could be a good thing for some DAPs, and a bad thing for the IEM, depending on the gears). but in any case it's not an ideal situation, consider that to be a band-aid until you decide who to sacrifice, the DAP, the IEM, or maybe both once like me, you're become a fully fledged hiss parano.