Again, from Foreman’s bel canto Method:

Theoretical Discussion: As mentioned before, the difference between solfeggi and vocalizzi is not well-defined. Solfeggi are to be sung with the solmization syllables as shown below. Vocalizzi are intermediate pieces preparatory to working on arias, and sung on [a] or [e]. (Most teachers recommend avoiding [i] and [u]; Mancini and Manfredini advise familiarity with all the vowels.)

Corri

THE SOLFEGGIO Is the art of sounding the seven notes of the Gamut with the Syllables annexed to them, viz:

The following exercises, constructed on the Scaletta, may seem boringly simple, but if they are done painstakingly and with great care for the intonation of the intervals, they will help to keep the voice steady and accurate in pitch. They should be sung at a moderate speed, and a breath taken where necessary. [Author through end of “to mix intervals.”]

The reason for using the Fixed-do system in preference to “movable-do” is that solfège is a useful tool, not an obstacle, and the ear learns intervals more accurately if there is an anchor – the gradually acquired sense of where C is – to which all other pitches can be related.

For a little more challenge, and to introduce more difficult intervals, here are three versions of Mozart’s Exercizio per il canto, the original and two complications:

At this point the scholar is advised to acquire as much speed in solfèging as possible, consistent with clarity and easy articulation on the syllables. The following exercises, purported to come from Porpora, should be solfèged in as rapid a tempo as possible, and transposed for the easy range of the voice.

There are many other sources for solfeggi, and the more often the student practices with seven syllables in varying tempi and melodic shapes, the better. A random example from Aprile’s 36 Solfeggi is given here.

This is Aprile’s Solfège #1:

This is his #3:

And for a bit more challenge, #24:

Foreman, Edward. A bel canto method: or, How to Sing Italian baroque music correctly based on the primary sources. Vol. 12. Pro Musica Press, 2006.