They may negotiate for specific things, like Trump wanting the love letters from the North Korean dictator....the archives would make a duplicate, either for Trump or themselves.
BUT ALWAYS, WITH EVERY PRESIDENT, the National Archives maintains and holds the presidential records.
No president since Reagan and the new law on it, has taken all of their presidential records with them, and held on to them, themselves. The LAW requires the National Archives to hold them, securely. Any negotiation is done after they are in the Archive's possession.