No. And the fact that this question arrives as often as it does suggests the phrase couples massage is doing some quiet damage, because it implies one thing being done to two people. That is not what a couples booking is. It is two separate sessions that happen to be sharing a room and an ending time.
Everything inside those sessions is chosen independently. Technique. Pressure. Length of the opening conversation. Which therapist. How much talking happens before the room goes quiet. The only thing the two of you genuinely share is the hour it occupies and the state you come out in, and that second one is arranged by the therapists rather than by any agreement between you.
What different actually looks like
A common booking in this city, and one nobody in the room finds remarkable: one of you takes deep classical work through the shoulders and lower back, because of a flight or a week or a desk. The other takes something far slower, which is not about the back at all. Two therapists, one room, ninety minutes, two completely different hours.
Another: one of you has done this before and wants a specific technique you cannot easily get at home. The other has not and wants something gentler to begin with. That pairing works. It works better than two people ordering the same thing out of politeness, which is the version we actually try to talk couples out of.
Pressure is the one people underestimate. It is set on each of you individually and is rarely the same on both sides of the room, one therapist working at a depth that would be unbearable a metre and a half away, while the other stays light for the whole session. There is no reconciliation of the two. They simply run in parallel.
Choosing the therapists separately
The roster runs to forty-five people and the two of you can choose from it independently. Nobody is required to take a matched pair, and there is no version of this where a preference gets vetoed by a partner's preference. If one of you wants a particular therapist and the other wants someone quite different, that is two names in one booking message and it is completely ordinary. The therapists page is there to be read by two people disagreeing amiably.
What we do ask for is both sets of preferences, explicitly, rather than one person's preferences applied twice. A message that says what one of you wants and leaves the other blank produces a session where one half was designed and the other half was guessed at. That is the single most avoidable way a couples booking underdelivers.
The one thing that is shared
The clock. The pair agree their running order beforehand and watch each other's progress from the halfway mark, so however different the two sessions were, they stop within a minute or two of one another. This is the actual reason to book a pair rather than two appointments on separate evenings. Two people who wanted different things, and got them, are still left with the same quiet room once the hour is up.
There is a version of this where wanting different things does cause a problem, and it is worth naming: when one of you does not want it at all and has agreed in order to be agreeable. That is not a difference of preference, it is a difference of consent, and no arrangement of the room solves it. Everything short of that, different techniques, different pressure, different therapists, different levels of enthusiasm, the room handles without comment.
If you are trying to work out what the two halves should be, the couples booking page sets out how the two sessions are run side by side, and the questions page covers the rest. There is no published menu here that the two of you have to choose from together. There is a conversation, held twice.