I just don't think that this is a question that can be answred in a forum post. Your better off getting it strait from the horses month, and ask Matt in billing by submitting a ticket.
Cancelling Diamond Membership Account

Of course a cancellation becomes effective only to the end of your current paid period. Just click the "Cancel" link in your account and see. Don't worry, just don't click the "YES - please cancel" button on the next page if you don't want to do it for real ...

What do you mean by "the end of your current period?" If someone starts in the middle of October and has paid up to the middle of Oct of 2014, can he get credit if he decides to open a new account, let's say next month?

That breeds a lot of suspicions; Why would you want 2 accounts??, unless you have a child who uses the same computer.

I mean if you were to cancel your subscription now you'll still have a Diamond membership until October, but it won't renew again. So there's nothing to give credit for.
If you downgrade say to Platinum you get credit for the percentage of your Diamond you didn't use and your Platinum will be paid for that much longer.

I never said 2 acccounts. One gets cancelled. A month or so later, you open another by using the credit you have plus a few dollars more in order to start all over again with a full account.
Is that feasible?

By the way, this was just a question to get some people riled up... I'm sure no one has ever done this before.

Economically, it sounds perfecly feasible to me. Weather chess.com will go for it, is a different story. What creates suspicians, is you saying, "reasons are unimportant here". Did YOU cancell the account, or did chess.com cancell?? I only ask because recently, there's been a rash of impersonaters, cheaters, imposters,crooks, closed accounts; so chess.com doesn't need to waste time on the riff raff. The're trying to solve IT sanfus with the new apps, and make it a good site for everyone.
What happens if someone wants to cancel his diamond account early in his membership. Does he get credit for it?
Can he use that credit to start a brand new account? Reasons are unimportant here, just the facts... :-)