Do I need software to pair the M720 to a second Unifying receiver?

Yes, you need the Unifying Software to pair the mouse with a second receiver or to pair the mouse to another channel on the same receiver. The Unifying Software can be downloaded at http://support.logitech.com/software/unifying. One Unifying receiver is included in the box. (Page 5)

From the official Logitech M720 Mouse manual, page 5

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