We’ve not yet seen anyone compete the Jaeger with an extra salto. A recent article linked from Science of Gymnastics Journal analyzed the skill.
… From the data it can be concluded, that the double Jaeger is possible in either tucked or piked body posture …
Despite its feasibility, there may be … arguments why the Jaeger Salto on the high bar is not performed that often in international competitions, and potentially, why the double Jaeger may not be attractive for gymnasts to learn as compared to other release-regrasp skills.
… the Jaeger salto is a forward salto during which the athlete “sees” the high bar relatively late prior to regrasp, and therefore has less time to adjust the regrasp based on visual information, as compared to other flight elements, like the Tkatschev (Gervais & Tally, 1993; Raab, de Oliveira & Heinen, 2009).
… the athlete has to reverse the direction of his rotation when regrasping the bar, as compared to other flight elements, like the Kovacs Salto if he intends to perform a subsequent giant swing. …
Download the full research article – WHAT IT TAKES TO DO THE DOUBLE JAEGER ON THE HIGH BAR (PDF)
by Thomas Heinen, Damian Jeraj, Pia M. Vinken, Katharina Knieps,
Konstantinos Velentzas & Hedi Richter