A couple of places I go do this. It's like they work as a team. They have different roles. Maybe the phase of the moon plays a part. Maybe a regular comes in and wants a specific therapist. I'm sure there are things I don't understand.

I think I sort of caught the massage therapists at a local AMP (Asian Massage Parlor) off guard about 18 months ago with my strange request. It wasn't them switching up on me, it was me requesting that they switch up on me. Let me explain.
I had been going there for about a year, with maybe a month or two in  between my visits, so I had just over half a dozen visits total. I had my two favorite ladies whom I always requested, and if they were off duty or busy with another client or each had another client, I never went with any other therapists, I would just leave and wait until another day or night. At least two or three times I had them both massage me together, a four-hands massage. Over a period of time, definitely not from the first couple of visits, happy endings were silently "suggested" to me in sign language. I usually declined, becauseI like getting sucked and fucked rather than a handjob, but they never offered nor suggested other sex acts. I wanted to take that next plunge, but didn't want to get blacklisted or arrested, so I always chickened out. Eventually, I accepted and paid extra for the handjob twice, the first time in a solo session and once when they were both doing a four-hands on me. Both of the times I got the happy endings, the taller of them was the one who did the deed, in fact, when they were both in the room with me for four hands, Tall-One waited to mime the happy ending suggestion to me when Shorty left the room to go get the hot towel, I accepted thinking they'd both do me together. When Shorty came back with the hot towel, Tall-One said something to her in Mandarin, and then Shorty left the room again before Tall-One took me in hand and completed the task solo. Shorty never returned that evening, so I don't know if she just doesn't do or doesn't like "extras", or if she just didn't want to do them with me, or if it was Tall-One's turn at bat, or what.
Anyway, getting back on topic; switching. One night, I checked their availability, both of them were working, so I stopped by and first requested a 1-hour massage with Shorty. I then said I wanted Tall-One too, but for a second massage. The front counter lady, who spoke only rudimentary English, thought I wanted four hands. Technically, I told her I did, just not both ladies at the same time. She thought I meant I would leave after the first one and come back later that night for the second massage. She called Tall-One and Shorty to the front, they immediately recognized me and all three of them started jabbering away a mile a minute. My two ladies also misunderstood me, thinking I wanted the usual. I tried Google Translate, but that didn't work either. Their minds were wrapped around their normal procedures according to the menu, and no deviations made sense to them.
I finally got them to understand that as soon as Shorty finished massaging me, I would remain in place and she would leave, Tall-One would come in and begin a new massage from scratch. Still, they thought I would shower, dress, go back to the front counter and pretend I had just walked in and ask for Tall-One. No, no, no, no! Stay on the massage table naked as a jaybird except for the towel across my butt, one woman exit, next woman enter.
It finally happened just the way I wanted it to, but they were beyond flabbergasted and all out of sorts. They didn't want me to ask for that again, it confused them far too much. To me, I still don't see what the big deal is.
Alas, I never got a chance to find out if I could try it again, because that was my last visit there before the Corona Virus began. AMPs shut down, and even when they reopened, many people are avoided Chinese body-related services. I don't even know if the place is open, nor whether or not my two favorite ladies returned.