Naughty Dog once worked on a Last of Us Part 2 multiplayer mode, a datamine suggests.
YouTuber Specilizer found multiplayer assets in the game that point to a large multiplayer map, which they speculate could be for a Factions battle royale mode given the size of the map. Considering the development period and release date of the game saw the explosive rise of battle royale games like Fortnite and PUBG, it makes sense Sony would have wanted to explore the genre with a first-party title.
Other assets include a "Listen-Mode-Device", which could potentially be the way to use listen mode in multiplayer. There are also backpack and armour models specifically for multiplayer.
Naughty Dog previously stated that while multiplayer would not be included in the release of The Last of Us Part 2, the team had ambitions to release a separate multiplayer mode in the Last of Us world. There was, however, no timeframe for this release, and the announcement was posted back in September 2019. It's possible multiplayer plans were scrapped at the start of the pandemic as work was disrupted across the industry, not to mention the single-player game was already behind schedule.
But I wouldn't give up hope. We know Naughty Dog is working on a remake of The Last of Us. While the project is controversial among The Last of Us' fanbase, I would expect to see a new multiplayer mode come to fruition there given the original game's Factions mode. A team within Bend Studio is also helping Naughty Dog with a multiplayer game, which I wouldn't be surprised to find related to this.