A Black Box to Solve Everything

I am not aware of any commercial products intended for HiFi but I know of a guitar effects pedal, Mercury IV (harmonic boost), by Spaceman Effects that has a dial for generating even order harmonics. I imagine two could be used in dual-mono, which would meet the OPs requirements. They are on reverb for around $300. Something like the Switchcraft SC600 Dual Adapter Box would enable you to convert to 1/4" TS/TRS to RCA and back.  I own this pedal and love it for guitar.  The pedal can color or be transparent depending on the settings and gear on either end of it.

It isn't as simple as adding higher tube distortion. The Carver concept of transfer function actually works though, to  signmake a solid state amp sound like a matching tube amp, which is exactlly matching the electrical output of two amps. But I suspect the reverse won't work, matching a tube amp to a solid state one. Carver did the comparison matching one of his amps to I believe a Conrad Johnson. The listening panel agreed(after 2 tries I think). And I personally spoke to Gordon Holt and he confirmed that Carver suceeded. 

Don't use this one,

All the best,
Nonoise

About a year ago I watched a video (on YouTube iirc) in which Nelson Pass spoke about an amp he was working on, one that was intentionally designed to add harmonic distortion to the input signal. He also explained the rationale for doing so. I could be mistaken, but I think it may have been in an interview with Steve Guttenberg, recorded in Nelson's listening room.

Nelson Pass's DIY Nutube preamp kit allows for adjustment of distortion. Here is a description from the design document:

"The attraction of the Nutube in an audio circuit is the Triode character, allowing adjustment of the distortion by operating the device in a specific voltage/current load line. For a given amount of current through the tube there is a point at which the square law effects of Cathode current and Plate voltage cancel, nulling out 2nd harmonic distortion and leaving 3rd harmonic. This is the lowest output distortion setting.

If you increase the Plate voltage, the circuit takes on a positive phase 2nd harmonic distortion character, and if you lower the Plate voltage it has negative phase 2nd harmonic. These distortions increase as you adjust the Plate voltage farther from the null point"