Want to upgrade HDD but don't want to lose P.T.

I grabbed P.T. back when it was available on the store and I has lived on my PS4 since. I play it sometimes still, but mostly it's a collection / novelty thing. That said, I'd like to keep it after upgrading to a larger HDD. Is this possible, and if so, what steps do I need to take. I know that I shouldn't clone the existing drive due to the way PS4 partitions the drives.