A Black Box to Solve Everything

I guess you could try a unity gain tube buffer which is normally used for impedance matching between components, I remember reading somewhere there was even a SS device which emulated the 2nd (and others?) harmonic of a tube and the distortion (magnitude of harmonic) was applied in variable steps. I can't recall where I have seen it, I will have a search.

Such digital signal processors already exist.   I've seen them and used them.   They can mimic tubes, all sorts of distortion, and create a unique sound in many ways:

The secret of the perfect sound

I'm not trying to be a wet blanket here, but why would I add another component in the chain? I happen to own multiple tubes, so play what you have, and be happy! JMO.

For you DIYers, Ethan Winer provides directions on how to build his Mojo Maestro box, which he states is: "...a simple box that can add distortion ranging from very subtle—to add a little grit to a sterile sounding instrument track or to help “glue” a full mix together—through severe clipping to add “mojo” or “dirt” to any musical source that will benefit. The Mojo setting also switches in a capacitor to gently roll off the highest frequencies to counter the added buzziness. With gentler settings, the overall effect is similar to running music through a tube amplifier or an analog tape recorder but without the added tape hiss and flutter.": https://audioxpress.com/article/you-can-diy-build-the-mojo-maestro

Many of us have used tube preamps with SS amps to bring some desirable tube qualities to our systems, and others use SS preamps and tube amps. In 1973 as a college kid I ran a PAS3x with an H-K Citation 12.  Later a Motif FET pre with av MV55 amp.  All worthy experiences.  There is no single silver bullet, for this or any other system voicing conundrum.