BG Chap 13 - The puruṣa para in the body

In the body there is another person different from the jīva (paraḥ), who is the great lord (maheśvaraḥ), the supreme ātmā (Paramātmā). He is a witness (upadraṣṭā). He is situated close to the jīva and is the permitter of the jīva’s actions, the supporter and protector of the jīva. He gives permission (anumantā), for without His permission the jīva can do nothing at all. Although the Lord had already said that He is everywhere, He says this again to emphasize that He is also situated with the jīva. The word parama in Paramātmā indicates a personal expansion of Lord distinct from the jīva in order to defeat those who say there is one soul only.

Hrdyanananda Maharaja writes:

Here Kṛṣṇa has described both the individual soul and the Lord as puruṣa—persons—but the contrast is striking. The individual soul is a puruṣa, but he is (a) “situated in material nature,” (b) “trying to enjoy the material qualities,” and thus (c) compelled by his attachments to those qualities to take birth in high and low species of bodily encagement. In the very next verse, the Lord describes Himself also as puruṣa, but the
difference between the two purusas could not be more clear, for Kṛṣṇa is said to be the supreme or transcendental puruṣa (puruṣa para˙). The use of the adjective para˙ to denote the supreme puruṣa is significant, for this
word not only entails the notion of supremacy, but also a strong sense of “the other.” Indeed, para is often used in Sanskrit to indicate the opposite of atma- or sva-, both of which indicate “self” or “one’s own.” In fact, atma
in Sanskrit is the simple reflexive pronoun. In other words, para has the unequivocal sense here of the wholly other who is supreme. In this same verse, Lord Kṛṣṇa also uses the term paramatma, describing Himself thus as
the “Supreme Soul.”

It should be noted that the adjective parama (used with atma to form paramatma) is almost identical to para in conveying supremacy, but that parama does not convey the sense of being the “other” in contrast to one’s
self. It is this wider term para that Kṛṣṇa employs to distinguish Himself, as puruṣa, from the ordinary puruṣa who is struggling vainly to exploit the Lord’s material creation. Thus the Gita’s claim that the individual soul is
eternally distinct from the Supreme Soul is a strong one, and not a vague or esoteric articulation.