Chp 8 of the Song of Songs is a dialogue about love and this chp closes it off. As I have worked through this text I think the three-character interpretation does have merit — but it is not entirely clear. If you read chp 8 carefully it ends with clear reference to Solomon (v. 11), and it is not clear to me that he is the one being invited to the bed.
Furthermore, in 8:11 the shepherd speaks and speaks of Solomon — and the lines of 8:12 are damning of Solomon’s lifestyle: “My own vineyard is before me [my love, my wife]; the thousand [vineyards, lovers] for you, Solomon.”

So, with this in mind — that the man and woman make a choice of fidelity against Solomon’s rash and senseless wooing of yet another woman to his harem — we come to chp 8.
Her mood has changed. The constraints of society for a wife and husband not to be effusively affectionate in public irritate her — O how I wish you were like a brother to me. For I can be affectionate with a brother [not as with a husband, of course, but still more publicly affectionate] in public.
And here we enter once again into the make-believe or fantasty world of the Song — is this reality? is this a fantasy? The blurring of the distinction is noticeable in the Song. By verse 2 she has formed union with her lover.