2 player multigames

Hey PS community, hope you can help me with some questions.

I have 2 Playstations 4's (a 4 and a pro), now i have a friend that will live with me for some days.

Can we play together. Playing each on a different PS, the playstations are on the same LAN (With Cable) and use the same username to log on to playstation plus.

If we can what games are fun to play.