Not to hijack this thread, but do you know what gives them that artificial warmth (bump in the mid range?)
I used to think "warm" meant a boost in the upper-bass range, but to some people it means slight "desirable" distortion. So I usually try to avoid this kind of terminology, or like you, explain exactly what I'm talking about.
A headphone's frequency response is determined by its electro-mechanical and physical properties. I don't know exactly what contributes to the midrange or mid-bass bump. It's obviously not "easy" to make a headphone with flat frequency response, or one that tracks the Harmon preference curve, but it's also obviously not super-expensive.
and how can I add that to more neutral headphones?
You can tweak the frequency response with
equalization. There are software & hardware equalizers.
You have to be a bit careful with boosting because you can drive the amplifier or headphones into distortion (especially if you are already listening "loud"). Or with digital EQ you can push the digital levels into digital clipping although most software equalizers have a volume/gain adjustment to lower the overall level.
Thought of getting a tube amp and/or something like the Schiit Lokius or Loki Max to fix that.
Probably not...
If your headphone amp has a high output impedance, the frequency response of your headphones will be altered... A bump in headphone-impedance at a certain frequency will make a bump in frequency response at that same frequency. (Headphones are tested & specified with a low-impedance "constant voltage" source.) It's all relative and it happens to a lesser extent with high impedance headphones and
it doesn't happen at all with a good headphone amp, which will have low output impedance.*
If the headphone amp has high output impedance
and the headphone has a bump in impedance in the mid-bass range that
might work. Some people get that effect and they like it. But, the headphones probably have other impedance variations and you probably won't get the "right amount" of boost at the "right frequency". (Technically, it's not "boost"... It's a drop where the impedance is lower but it's a
relative boost where the headphone impedance is higher.)
Tubes to
tend to have higher impedance than solid state electronics but in a hybrid amp the tube probably isn't at the output stage driving the headphones. With tube power amplifiers (for driving speakers) the audio goes-through an impedance-matching transformer between the tubes & speaker. The transformer can potentially add its own distortion and frequency response variations in addition to any potential tube distortion. I don't know if any "modern" tube headphone amps have a transformer.
* You don't normally get a published output-impedance spec. Usually they give you the recommended minimum
headphone impedance. The amp's impedance should be much lower.