The man's final mutanza in Caroso's passo e mezo (in Il Ballarino) calls for four "seguiti trangati in aria semidoppii". Alas, Caroso doesn't define any such step, and nor does anybody else (that I recall).
Caroso does describe a "seguito trangato" (three steps and a zoppetto, raising the foot behind) and a "seguito semidoppio" (two steps and a seguito spezzato). Other steps are done "in aria" - meaning that there is a small jump incorporated, at some point (e.g. passi in aria, aka passi in gagliarda). So, what to do?
Seguito trangato seems naturally to come "in aria"; one could emphasise that if one wished. It's not obvious how to make do a seguito semidoppio "in aria", nor how to combine a seguito trangato with a seguito semidoppio.
This lead me to ponder what makes a seguito semidoppio semi-doppio. A doppio, as described by Caroso, is three steps followed by joining the feet together, with a falling-rising-falling motion (bend knees, raise then lower heels). So what is "semi-doppio" about two steps followed by a spezzato? A spezzato could be described as joining the feet together with a rising-falling motion (raise then lower heels) - perhaps a seguito semidoppio is a seguito with a rising-falling ornament at the end, half the ornament of a doppio, which finishes with a falling-rising-falling shape.
From there, I considered that a seguito might be considered "semidoppio, in aria" if it has that same shape at the end - rise-fall - without necessarily having identical movements to a seguito spezzato. So perhaps a seguito trangato - step, step, step, zoppetto raising the foot behind - followed by a rise-and-fall on the toes, or including one? David, my partner, proposed something like a sottopiede as a "spezzato in aria".
So there are many pleasing and plausible answers, and I'm still experimenting.
My ideal solution will: