Platonic sex magic - isn't that a contradiction in terms? I guess that depends to a small degree on your personal definition of "platonic". Officially, the definition relevant to us is that of platonic love: "of, relating to, or being a relationship marked by the absence of romance or sex". So, if we take the word "sex" to mean intercourse, then there's no real contradiction. Dion Fortune, amongst many others, recognised that, in fact, neither intercourse nor orgasm are necessary for sex magic. Her biographer, Alan Richardson, comments that "because intercourse did not occur, this did not mean that sexuality was absent from the workings".
The same was true of the mediæval love mystics, the Courtly Love movement and many others: the important parts are the psyche and the sense of arousal which induces changes in consciousness. To what extent you consider that sexuality and sensuality constitute "romance" will vary from person to person, so I'll use the term "Courtly Love" to imply a relationship that fits within the bounds that would have been recognised at the Courts of Love. Whilst it may include sexuality, sensuality and indeed the recognition of arousal, the relationship does not include intercourse, orgasm or touching with the direct intention of arousal. It certainly worked eight hundred years ago and whilst the simple fact that a technique is hundreds of years old doesn't always make it valid, in this case it is - in the right frame of mind, it's perfectly possible to work sex-magic, with a partner, without actual physical sex. How might this be?
Well, if you've worked on a symbol system which takes you into the same frame of reference, and the triggers are all in place, then sharing those symbols and triggers can work in the same way as physical intercourse. You need to work at it, but the end result is the same as attuning the mind in such a way that the Great Rite in token actually works. Think, for example, of dancing together, or of flirting or even sharing a meal. Both give some sense of the same feeling, of taking pleasure in each other, without making physical sex a particular objective.
One way to work would be to practice the basic techniques and work through the solo exercises to build up the imagery - I'm using a well, but it could be anything else which works for both of you. Discuss and share the imagery so that you're both familiar with it (but remember that there's no "right" answer). Now, you should be able to use the breathing exercise to work together just "as if". Treating something "as if" it's true is another basic technique.
Dion Fortune's group simply held hands. This is about as platonic as it gets and I'd make a word of warning here. The further you move away from an obviously ritual context, the more carefully you need to consider the mental effects, and especially the triggers, you're using. Fortune's group used the index and second fingers outstretched to make a blade, surrounded by a fist to represent the chalice. Simple enough (in action at least), but they still took the precaution of using additional special contexts. I've said it elsewhere but it bears repetition: ensure that you group the symbols together so that you're saved the embarrassment of dropping into trance whilst shaking hands with the person who has just bought your firm.
Having worked on the imagery, the reaction will be there. Use the breaks in time and space to which you have become accustomed, come to each other in full recognition of your sexuality, and the feelings of the heart will do the rest. That sounds sickly-sweet and may seem trite: it is nonetheless true. This is not a poor substitute for intercourse in sex-magic, nor is it superior: it's just different.
Various people have "called" me on this, Apart from recommending the Magical Diaries of Dion Fortune, Colonel C R F Seymour and Christine Campbell Thomson, selected parts of which are available in modern editions, I felt it behoved me to rise to the challenge. The results were two rituals (or pathworkings, as you see fit), Procession of the Hidden Hallows and The True Cup, that may illustrate the point. The former includes ritual nudity, so for many people it will fall outside the definition of "Courtly Love", but there are two reasons. Firstly, it does maintain a clear ritual context and secondly nudity isn't a universal taboo. The latter is worked clothed, but thus requires significantly more care in generating the ritual triggers. Each is designed to generate a specific mental state, so if you decide to mix and match, please let me know how you get on.