Whilst No Man's Sky did not start its life as a multi-player game (in-fact it was designed to be lonely); it has evolved to include a great deal of multi-player elements.

Players can naturally encounter each other in the wild (called Ambient multi-player). This is unlimited, but if too many players meet in the same place, the game's frame rate can suffer as a result; and base parts can struggle to load in. For reference; I once participated in a group photo in-game. We had 100 people there. The frame rate was mostly OK, very little slow-down; but the base was too complicated for all the parts to load for everybody. A second try with very few base parts worked just fine.

They can also do missions together from the Space Anomaly's Nexus in groups of up to four, choosing from the 16 players there.