Hello Lewis Put,
I think you are referring to the Furano-Beie ticket, offered by JR Hokkaido. Please note that we at jrpass.com only focus on the nationwide JR Pass. While I also try to help visitors with other kinds of questions where possible, I don't have the exact answer to your question and recommend contacting your point of sale or JR Hokkaido for this.
You can find all the information about this pass here:
http://www2.jrhokkaido.co.jp/global/english/travel/
That said, I the website states that you are allowed unlimited travel within the validity period/area.
Hope this helps,
Daniel