You want to upgrade the SSD.
I upgraded to a 2tb Corsair SSD (remember when you could just buy stuff? For reasonable money?). When I copied stuff over, I started out with the Corsair in an external enclosure. The card crashed during the copy, and I think the reason why is that these cards are dramless. They borrow ram from the host, and when you're in an enclosure the "host" has no ram to give. What I had to do was put the new card in the deck, install a steamos recovery on it, put the old card in a reader, and copy in from there.
Uhh I'll leave the details of copying to everyone else, but just know that writing to an external nvme enclosure can give you a bad time.