I'd say possible, but very unlikely.
Requesting a transfer to another unit was possible, but I think limited. I've only ever seen it within the same Division when they were all the the same general area. A direct transfer between theaters (UK/NW Europe to Italy) seems unlikely.
Could happen by chance if a man left his unit and went into the general reinforcement pool and then was posted to another theater with a large group of other reinforcements, but for it to happen to both brothers is unlikely. This would also presume that the Argyles didn't try to get them back in this scenario. Since they appear to have been long time Argyles, they would have wanted them back if they were efficient soldiers and there would be an Army bias to send men back to their original unit.
The way to find out for sure is to get their records and see their actual movements.