Triple conjunctions between Mercury and Venus are also possible when they are passing between Earth and the Sun at the same time.
In the events in which Mercury is involved, the second conjunction is invisible because of small elongation from Sun; both other events are difficult to see because of the nearness to horizon and the relatively low brightness of Mars, which is there always near its greatest distance from Earth, barely visible.
For a Mars–Venus triple conjunction all three events can almost always be seen, but Mars is dim because of its great distance from the Earth.
The most historically important triple conjunction was that one between Jupiter and Saturn in 7 BCE-5 BCE, which has been proposed as the explanation for the star of Bethlehem.
They are unspectacular, but offer a good possibility for amateur astronomers to find these dim planets.
Triple conjunctions between planets and bright stars close to the zodiac are not so frequent (approximately 2 events in 10 years).
Note that conjunctions in right ascension and ecliptic longitude need not take place on the same date.