I computed all triple shadow phenomena of the major moons with their planet from 1000 CE to 3000 CE. I found 315 of such phenomena occurring on Jupiter, 303 on Saturn and 151 on Uranus. During the 2001 year period Saturn experiences 1 quadruple shadow phenomena meanwhile Uranus experiences 3 of such. I computed all shadow events of the Galilean moons with Jupiter, their mutual eclipses and the planet’s elongation from 1000 CE to 3000 CE with Occult 4.10.1.0 (files updated: 2020 March 20). I repeated the same procedure for Tethys, Dione, Rhea, Titan and Iapetus with Saturn and Miranda, Ariel, Umbriel, Titania and Oberon with Uranus. I then filtered the results to find triple and quadruple shadow events within the satellites and their respective primaries. Finally, I added the planet’s elongation for the event’s date above found and mutual eclipses only occurring during a triple or quadruple shadow event on the planet. I assumed that the Gregorian calendar commenced in 1582 October 4. Before that date, I used the Julian calendar. All times are in Universal Time. Minutes are rounded to the nearest tenth of a minute. For convenience, I used Arabic numbers to designate all satellites instead of Roman ones.

{"references": ["Steyaert, Christian (1979). Jupiter and triple shadow phenomena, Journal of the British Astronomical Association 90:42", "Meeus, Jean (2002). Jupiter: triple satellite phenomena, Journal of the British Astronomical Association 112:287"]}