A family of Microsoft word processing software products for creating web, email, and print documents.
The other side of the badges will be a second page printed on the other side of the stock. I would deal with this on the data side by having the information from the first page of data duplicated in for the second page, keeping in mind how data is arranged in a label mail merge.
In a label mail merge the data is displayed:
A B
C D
E F
G H
You would want the second page data to be in the order: BADCFEHG
Another way to handle this would be to print the badges:
A A
B B
C C
D D
You would only print on one side of the badge and fold vertically.
Doug Robbins' Merge Tools may have something to deal with this directly but there is nothing in Word itself to handle it.