"Can I get more than 1 Office 365 Personal Subscription if I have more than 1 qualifying device?
Yes, you can. You can redeem the offer for every new Lumia 640 or Lumia 735 phone you have purchased during the offer period.
Why can’t I get the Office 365 Offer?
This may be caused by the following reasons:
...
Your Microsoft account has already been used to activate the offer
..."
I successfully installed the second Office 365 Personal on another PC using the same MS account. This is more useful to me than a second year.
An Office support tech told me using the second key would not add another year to the existing subscription, but to be honest I got the feeling he really didn't understand the question.
PS: It doesn't look like they double the OneDrive storage even though I have two subscriptions.