The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut [1896] at sacred-texts.com
15. The entering (of one soul into several bodies) is like (the multiplication of) the flame of a lamp; for thus scripture declares.
Under Sûtra 11 it has been shown that the released person is embodied. The question now arises whether the bodies which the released create for themselves when rendering themselves threefold and so on are soulless like wooden figures, or animated by souls like the bodies of us men.--The pûrvapakshin maintains that as neither the soul nor the manas can be divided they are joined with one body only, while the other bodies are soulless.--To this the Sûtrakâra replies, 'Like the flame of a lamp is their entering,' i.e. just as the one flame of a lamp can pass over into several flames (lighted at the original flame), because it possesses
the power of modifying itself, thus the soul of him who knows, although one only, multiplying itself through its lordly power, enters into all those bodies. For scripture declares that in this way one may become many, 'He is onefold, he is threefold, fivefold, sevenfold' (Kh. Up. VII, 26, 2). And this is not possible, if we should accept the simile of the wooden puppets, or the entering of other souls into those additional bodies 1. Nor again can there be any motion on the part of bodies destitute of souls.--Nor is there any force in the objection that, because the Self and the Manas cannot be divided, they cannot be in connexion with more than one body. For the Self, because possessing the quality of having true wishes (i.e. wishes which become real), may be supposed to create other bodies with internal organs, conformable to the original one organ; and, the Self dividing itself through the division of its limiting adjuncts, it may be possible to give a soul to each created body. This is the topic which the books on Yoga treat, in the chapters explaining the connexion of one soul with several bodies.--But how can lordly power, enabling the released soul to enter into several bodies, be admitted, if we consider that different scriptural texts declare that the soul in that state has not any specific cognition? so e.g. 'Whereby should he know another?' 'For there is then no second, nothing else different from him that he could know;' 'An ocean is that one seer, without any duality' (Bri. Up. II, 4, 14; IV, 3, 30; 32).
To this objection the next Sûtra replies.
413:1 See Pûrva Mîmâmsâ-sûtras II, 3, 5th adhikarana.
414:1 I.e. the scriptural statement about one Self rendering itself manifold can neither be reconciled with the hypothesis of the other bodies being moved by the one soul as puppets are moved by one person through strings, nor with the hypothesis of a new separate soul entering each new body.