The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut  at sacred-texts.com
6. But (there are also, in addition to the seven prânas mentioned,) the hands and so on. This being a settled matter, therefore (we must) not (conclude) thus (viz. that there are seven prânas only).
In addition to the seven prânas scripture mentions other prânas also, such as the hands, &c., 'The hand is one graha and that is seized by work as the atigraha; for with the hands one does work' (Bri. Up. III, 2, 8), and similar passages. And as it is settled that there are more than seven, the number seven may be explained as being contained within the greater number. For wherever there is a conflict between a higher and a lower number, the higher number has to be accepted because the lower one is contained within it; while the higher is not contained within the lower. We therefore must not conclude that, in deference to the lower
number, seven prânas have to be assumed, but rather that there are eleven prânas, in deference to the higher number. This conclusion is confirmed by one of the passages quoted, 'Ten are these prânas in man, and Âtman is the eleventh.' By the word Âtman we have to understand the internal organ, on account of its ruling over the organs. Should it be objected that scripture also mentions numbers higher than eleven, viz. twelve and thirteen, we admit that, but remark that there are no objective effects in addition to the eleven (well-known) objective effects on account of which additional organs would have to be assumed. There are five distinctions of buddhi having for their respective objects sound, touch, colour, taste, and smell, and on their account there are the five intellectual organs; again there are five classes of action, viz. speaking, taking, going, evacuation, and begetting, and on their account there are the five organs of action; finally there is the manas which has all things for its objects and extends to the past, the present, and the future; it is one only but has various functions. On account of the plurality of its functions we find it designated by different terms in different places, as manas or buddhi or ahamkâra or kitta. Thus scripture also after having enumerated the various functions such as desire, &c., says at the end, 'All this is manas only.'--That passage again which speaks of the prânas of the head as seven means four prânas only, which on account of the plurality of their places may be counted as seven; viz. the two ears, the two eyes, the two nostrils, and speech.--Nor can it be maintained that there are in reality only so many (i.e. seven), the other prânas being mere functions of the seven; for the functions of the hands and so on are absolutely different (from the functions of the seven senses admitted by the pûrvapakshin).--Again, in the passage 'Nine prânas indeed are in man, the navel is the tenth,' the expression 'ten prânas' is used to denote the different openings of the human body, not the difference of nature of the prânas, as we conclude from the navel being mentioned as the eleventh. For no prâna is known that bears the name of navel; but the navel as being one of the special abodes of the chief prâna is here enumerated
as a tenth prâna.--In some places so and so many are counted for the purpose of meditation; in other places so and so many for the purpose of illustration 1. As the statements concerning the number of the prânas are of so varying a nature we must therefore distinguish in each case what the object of the statement is. Meanwhile it remains a settled conclusion that that statement which makes the prânas to be eleven is authoritative, on account of the objective effects (being eleven also).
The two Sûtras (referring to the number of the prânas) may be construed in the following manner also. The prânas are seven because scripture mentions the going (gati) of seven only, 'When he thus departs life departs after him, and when life thus departs all the other prânas 2 depart after it' (Bri. Up. IV, 4, 2).--But, it may be objected, this passage says 'all the other prânas;' how then does it declare the going of seven only?--The Sûtra replies, 'on account of their being specified.' Seven senses only, from seeing up to feeling, are specified there because so many only are under discussion; as we see from the enumeration given in the passage, 'When that person in the eye turns away then he ceases to know any forms. He has become one they say. he does not see' &c. The word 'all' refers here only to what is under discussion, i.e. only to the seven prânas mentioned before, not to any other. Analogously when we say 'all the Brâhmanas have been fed,' we mean only those Brâhmanas who have been invited and concern us at the time, not any other.--If it be objected that the passage quoted mentions understanding (vigñâna) as the eighth thing departing, and that we therefore have no right to speak of the departing of seven only, we reply that manas and understanding differ not in essential nature but only in function, and that on this account we are entitled to speak of seven prânas only.--The answer to this
pûrvapaksha is as follows.--In addition to the seven senses, other prânas also, such as the hands, are known to exist, as we see from such passages as 'The hands are one graha,' &c. (Bri. Up. III, 2, 8). By their being a graha (seizer) is meant that they are bonds by which the individual soul (kshetragña) is tied. Now the individual soul is tied not in one body only, but is equally tied in other bodies also. Hence it follows that that bond called graha (i.e. among other things the hands) moves over into other bodies also. Smriti also ('He--the Self--is joined with the aggregate of eight, comprising breath, &c. 1, as his mark; his bondage consists in being bound by it, his release in being freed from it') shows that the Self is, previous to final release, not freed from the bonds called grahas. And also in the enumeration of the senses and their objects given by the Atharvana Upanishad ('The eye and what can be seen,' &c., Pr. Up. IV, 8), the organs of action such as the hands and so on, together with their objects, are specified as well, 'the hands and what can be grasped; the member and what can be delighted; the anus and what can be evacuated; the feet and what can be walked.' Moreover the passage, 'These ten vital breaths and âtman as the eleventh; when they depart from this mortal body they make us cry' (Bri. Up. III, 9, 4), shows that eleven prânas depart from the body.--Moreover the word 'all' (which occurs in the passage. Bri. Up. IV, 4, 2) must, because connected with the word 'prânas,' denote all prânas, and cannot, on the ground of general subject-matter, be limited to the seven prânas; for a direct statement has greater force than the subject-matter. Even in the analogous sentence, 'all Brâhmanas have been fed,' we have, on the ground of the words, to understand all Brâhmanas living on the earth; but because it is impossible to feed all Brâhmanas in the latter sense, we accept that meaning of
[paragraph continues] 'all,' according to which it denotes all invited Brâhmanas. In our case on the other hand there is no reason whatever for narrowing the meaning of 'all.'--Hence the word 'all' includes all prânas without exception. Nothing on the other hand prevents the enumeration of seven prânas being taken as illustrative only. It is therefore an established conclusion, resting on the number of the effects as well as on Vedic statement, that there are eleven prânas.
82:1 Sapta prânah prabhavantîty âder gatim âha kvakid iti, ashtau grahâ ityâder gatim sûkayati gatim iti Ân. Gi.
82:2 I.e. seeing, smelling, tasting, speaking, hearing, feeling, and the manas.
83:1 The eightfold aggregate of which the Self is freed in final release only comprises the five prânas (vital airs), the pentad of the five subtle elements, the pentad of the organs of intellect, the pentad of the organs of action, the tetrad of internal organs (manas, &c.), avidyâ, desire (kâma), and karman.