The original post that the "Improved persistent login cookie" refers, (found here: http://fishbowl.pastiche.org/2004/01/19/persistent_login_cookie_best_practice/) states:
The cookie should consist of the user's username, followed by a separator character, followed by some large random number (128 bits seems mind-bogglingly large enough to be acceptable). The server keeps a table of number->username associations, which is looked up to verify the validity of the cookie. If the cookie supplies a random number and username that are mapped to each other in the table, the login is accepted.
At any time, a username may be mapped to several such numbers
So, the user can have many persistent tokens at the same time.