Is there any way to transfer licenses/games between accounts or have multiple accounts with access to the games?

I recently bought a PS4 for $150 from an acquaintance that came with a few digital games. Obviously, those games are on his account; he's primarily a PC gamer and said he tried the PS4 for a few exclusive games but has no desire to stay with it now that he's finished them.

I have an existing PlayStation Account with some games on it and would love to buy some new ones as well, but ideally, I don't want to lose access to the handful of games that are already on this system. Is that possible, or will adding my account to this system result in me losing the games that came with it? Is it possible to still have access to those games while being primarily logged in to my account?