Robert Gjerdingen used to have a website called monuments of Solfeggi.
While it seems that website is no longer maintained the Achieve-It service has a saved copy...
If I follow the overview, solfeggi include a bass part with the melody. The website links to collections from 9 composers. 8 of the 9 collections include bass parts.
If solfeggi were mostly for instruments that couldn't play chords - voice, violin, flute, etc. - then it makes sense there wasn't a focus on improvising an additional part. I think the idea was to sing/play the exemplar melody and hear it in context with a good bass. I suppose a big part of it was to learn by doing things like resolving leaps or non-chord tones, tasteful ornamentation, etc.
I can see one obvious problem trying to work backward from the rule of the octave and applying it to the treble instead of the bass. While from the bass there is basically one chord type per scale degree, from the treble there are several chord choices...
The only repeated chord choice above the bass is the tonic repeating at the octave.
But look at the chord choices for the treble tone
DO, there are four different chords.
Notice also that linear direction alone doesn't clarify the melody choice as it does for the bass. Example, how to harmonize
FA in the bass. The linear direction between
MI in the bass determines the harmony,
I6 IV and
V4/2 I6. Compare that to how to harmonize
DO in the treble.
TI ascending and descending can be harmonized two ways.
I don't mean the rule can't be applied to the treble. Only that the choice are more complicated than compared to the bass.
I played from this solfeggi set this morning...
...and I can't get over feeling that the two part part writing between treble and bass was a major focus of solfeggi. At least a certain type of solfeggi. The bass was there as an exemplar, and the counterpoint was meant to be studied.
When considering both partimenti and solfeggi the bass and treble parts were given in the lesson. Of course partimenti lacked the treble (exluding partimenti fugue) and apparently some solfeggi didn't give the basses. But when it comes to improvising harmony, it seems to me, that part was the filler of inner voices not the proper bass or treble.
I suppose a bass can be improvised for a solfeggi without a bass, but it would be a different category of part: a proper bass versus inner voices.