Pressing M in
w3m launches the 1st external browser, 2M the second. While it is easy to bind the built-in command
EXTERN to another key, is it possible to bind the second to another key?
No, this isn't possible. There is only a single EXTERN command, and it invokes the first, second or third browser depending on the preceding numeric argument. W3m doesn't have a macro facility: you can't bind a key to a sequence of commands.
You could use an external macro facility: have a key send