You can have multiple message views, but you must rename the view
buffer and detach it to stop mu4e from reusing it when you
navigate up or down in the headers buffer. If you have several view
buffers attached to a headers view, then mu4e may pick one at
random when it has to choose which one to display a message in.
To detach the message view from its linked headers buffer, type z. A message will appear saying it is detached (or warn you if it is already detached.)
Detached buffers are static; they cannot change the displayed message, and no headers buffer will use a detached buffer to display its messages. You can reattach a buffer to an live headers buffer by typing Z.
You can freely rename a message view buffer – such as with C-x x r – if you want a custom, non-randomized name.
Detached messages are often useful for workflows involving lots of simultaneous messages.
You can tear off the window a message is in and place it in a new frame by typing C-x w ^ f. You can also detach a window and put it in its own tab with C-x w ^ t.