I think we need to consider what the signal is, and what 'distortion' is.
The signal is a system's internal representation of captured air pressure variations. It needn't actually be understandable by looking at it: it could be in
scrambled form, for example, or encoded or multiplexed in some other way. It could be transported as a stream of numbers. But it just so happens that in most audio systems, for at least part of the way it is represented as a voltage proportional to air pressure.
What can happen to such a signal on the way to the speakers is purely a by-product of it being a voltage transported through cables and other electrical components. Those side-effects are not acoustic, nor 'musical', in nature; they are
electrical effects i.e. in another domain from music and acoustics altogether.
The true hi-fi enthusiast understands this: the aim has got to be to get the signal through unchanged. Transformations of the
content of the signal are for the people who create it or, if trying to salvage a corrupted or poor existing recording, for specialists to use deliberate techniques to break the signal into its constituent parts and process those 'scientifically'.
That messing around with cables, transistors and diodes and the composite waveform might impart some meaningful
musical or
acoustic transformation of the content of the signal is a fantasy. Talking about distortion in the time domain as if it is distortion in the frequency domain ("second harmonic") is an example of this wishful thinking. All the magic box has done is maybe crush up the bottom of the electrical waveform and stretch out its top - a completely meaningless transformation in terms of music and acoustics. This transformation doesn't even attempt to analyse what is being represented in the signal, nor what a meaningful transformation might be for the contents of this particular signal.
If you think you are a euphonicist, consider: are you trying to change the signal, or the contents of the signal?
If it's the former, then what in the world of acoustics and music is 'a signal'? It doesn't exist. You are trying to change a meaningless internal by-product of an electrical system in order to improve your musical experience.
If it's the latter, what are you doing to access the contents of the signal in order to process them? Nothing. You are merely distorting 'the signal' without accessing its contents, and hoping that this will translate into something meaningful acoustically or musically. Again, an exercise in blind faith and wishful thinking.
At best, you may get a buzz (literally) from some sections of some recordings leading to you changing the music you listen to in order to pander to your system's foibles. At worst you corrupt everything you listen to with meaningless 'noise' (if only it sounded as good as noise) between now and when your critical listening abilities finally leave you.