The name of the class is worth unpacking. A mahapurusha is a great person, and the term has a long life in Indian religious literature outside astrology: Buddhist and Jain sources describe a set of bodily marks by which a great person is recognised, and the idea of an exceptional individual identifiable by physical signs is older than the astrological application of it.
The astrological handbooks draw on that vocabulary directly, giving each of the five yogas a physical description alongside its character, and Hamsa, the swan, is the Jupiter member. The swan carries its own weight in Indian imagery as a figure of discernment, and the association of Jupiter with the teacher and the priest is standard throughout the corpus.
The set is fixed at five because it is built from the five star planets. The Sun and the Moon are excluded, and the shadowy planets Rahu and Ketu, which have no signs of their own in the classical scheme, are excluded as well, so the class cannot be extended without departing from the rule that defines it. Where modern sources add a sixth, that is an addition and not a classical position.
The exclusion of the luminaries has a consequence for how the class is read. Because the Sun and Moon are the significators of the self and the mind in this system, a set of yogas built entirely from the other planets describes distinction in a particular sphere of action rather than the whole person, and the classical descriptions accordingly emphasise bearing, capability and reputation. That is a narrower claim than the name great person suggests.