Here is what Ranga Ramanuja, the Sri Vaishnava commentator on the Upanishads, says about this verse in this excerpt from his Mandukya Upanishad Bhashya:
yaḥ tat brahmaveda prītirupāpannadarśanasamānakārapāsanoyukto bhavatī - when he is endowed with Upasana which is of the character of vivid perception and which is of the form of love. brahmaiva bhavatī means ābhirvuta brāhmarupo bhavatī - he will become one in whom the nature of Brahman becomes manifested. Being freed from rāga, dveṣa and others caused by matter having the three gunas, he will manifest himself the eight characteristics of Brahman such as apahatapāpmatva etc.
So in Ranga Ramanuja's view the verse is talking about liberated souls manifesting the characteristics of Brahman, not becoming Brahman.
Ramanujacharya also touches on the verse in this section of his Sri Bhashya:
The objects of meditation in all the vidyâs which refer to the highest Brahman, are Brahman viewed as having qualities, and the fruit of all those meditations. For this reason the author of the Sûtras declares that there is option among the different vidyâs--cp. Ve. Sû. III, 3, II; III., 3, 59. In the same way the Vâkyakâra teaches that the qualified Brahman only is the object of meditation, and that there is option of vidyâs; where he says '(Brahman) connected (with qualities), since the meditation refers to its qualities.' The same view is expressed by the Bhâshyakâra in the passage beginning 'Although he who bases himself on the knowledge of Being.'--Texts such as 'He knows Brahman, he becomes Brahman' (Mu. Up. III, 2, 9) have the same purport, for they must be taken in connexion with the other texts (referring to the fate of him who knows) such as 'Freed from name and form he goes to the divine Person who is higher than the high'; 'Free from stain he reaches the highest oneness' (Mu. Up. III, 2, 8; III, 1,3); 'Having approached the highest light he manifests himself in his own shape' (Kh. Up. VIII, 3, 4). Of him who has freed himself from his ordinary name and form, and all the distinctions founded thereon, and has assumed the uniform character of intelligence, it may be said that he is of the character of Brahman.
The "Bhashyakara", by the way, is the ancient Vedantic philosopher Dramidacharya, whom I discuss here.