Not all equalizers work in the same way nor are all the same quality, and you'll always find compromises involved. Using a top class parametric equalizer like DMG Equilibrium, would provide the highest EQing quality but even using that high end piece of software, you have plenty of possibilities with regards to how the parametric equalization is applied. It's a relatively complex topic, but if you want to dig deeper, you can read the following manual:
https://dmgaudio.com/dl/DMGAudio_EQuilibrium_Manual.pdf
There you can find some extra information about IIR/FIR, about how some factors like phase comes into place when EQing, and more. There's much more to read, it's a relatively complex topic that might be considered of little use for the sake of just enjoying some good music.
On top of that there's the headphone natural response with its acoustic limitations. Pushing the transducer way out of its natural balance will increase distortion and degrade the overall sound quality. You can do +3dB broadrange boost using a quality parametric equalizer, that won't ruin sound quality. On the other hand boosting +10dB at 20hz will be much more tricky. Depending on the volume overexcursion might come into play, and that's no good for the drivers.
One more factor involved, when you boost certain frequencies, the amp will have to work harder to achieve that balance. If the amp is not good enough it will add unwanted distortion to the sound as well.
So yeah, it's not an entirely straight forward topic, but you can EQ without ruining sound quality. Try to find quality equalizers, and use them in a subtle way preferably.
Cutting is most of the times safer than boosting.
