Update: Naughty Dog spoke on Twitter following fan inquiries, adding that the solo campaign was by far the studio's most ambitious project.
Announced at E3 2018 by co-directors Anthony Newman and Kurt Margenau, the multiplayer mode for The Last of Us 2 was supposed to happen — as with the first title.
However, it seems that Naughty Dog's plans have changed, as announced by Emilia Schatz — co-lead game designer at the studio. It would seem that contrary to Naughty Dog's recent games, priority has been given to the solo campaign to favor the story and the direction.
The Last of Us Part II is scheduled for release on February 21, 2020, exclusively on PS4.