naked with naked, friend with friend, free with free
γυμνὸν γυμνῷ, φίλον φίλῳ, ἐλεύθερον ἐλευθέρῳ
I strongly suspect now that it is the saying transmitted from Theodore to Clement immediately before the Letter to Theodore was written. Maximus is here talking about bodies being naked, loved and freed. If we transform the original saying to its original context to what Theodore and Clement seemed to have known - viz. 'men' - the formula would read:
naked with naked, friend with friend, freeman with freeman
γυμνὸς γυμνῷ, φίλος φίλῳ, ἐλεύθερος ἐλευθέρῳ
Already to Theodore cites the first part of this expression - γυμνὸς γυμνῷ (Theod. III.13) in this form. Yet more interestingly now the second part of the formula - φίλος φίλῳ - is established in the LXX as a formula for God adopting a human being as a disciple.
We see Clement of Alexandria cite these very words in the very context that Maximus uses them - i.e. the need for the perfection of the flesh:
"Thou madest him a little lower than the angels." For some do not interpret this Scripture of the Lord, although He also bore flesh, but of the perfect man and the gnostic, inferior in comparison with the angels in time, and by reason of the vesture [of the body]. I call then wisdom nothing but science, since life differs not from life. For to live is common to the mortal nature, that is to man, with that to which has been vouchsafed immortality; as also the faculty of contemplation and of self-restraint, one of the two being more excellent. On this ground Pythagoras seems to me to have said that God alone is wise ... and that he himself was a philosopher, on account of his friendship with God. Accordingly it is said, "God talked with Moses as a friend with a friend" (Διελέγετο Μωυσεῖ ὁ θεὸς ὡς φίλος φίλῳ). [Strom. 4.3]
Chrysostom similarly identifies Adam's relationship with God as φίλος φίλῳ in his commentary on Genesis. Yet it has to be stressed that Clement is not citing from our LXX. The φίλος φίλῳ formula is completely absent.
The point is that everything will now come down to our ability to argue that Maximus's dissertation was originally directed against the Christian mysteries. The formula cited above must then have been connected with the Alexandrian ritual associated with LGM 1 (= the first addition to the longer Gospel of Mark). 'Naked with naked' is the preparation of baptism, 'friend with friend' identifies a state equal to Moses, 'freeman to freeman' represents the heretical ideal of escaping the bonds of the Law and thus being one 'greater than Moses.'