Hold the lens, shift the camera for multi frame pano stitching.
How about a proper perspective control lens mount configuration similar to the way Schneider impliments.
What does that mean?
As is now with Canon TS-Es, shift the lens one way, shoot a frame, shift the lens the other way while shifting the camera an equal amount the other way, shoot the second frame, then stitch.
But holding the lens limits you, effectively, to rear movements only unless you have a good geared head. Rear movements are nowhere near as useful as front movements.
Besides, this meme for shifting the camera not the lens is mostly spurious anyway, inducing parallax to the extent that PS, or any other stitching program, can't deal with it entirely automatically is not a simple task, you have to try pretty hard to actually create the problem. Not saying it can't be done, just that mounting the camera is the far better choice of the two.
I'd like to see some of your own actual images where parallax (the potential problem induced by shifting the lens not the camera) has caused any kind of issue with your image. It was very different when we were shooting film, but digital is so much more powerful.