How many primary keys can a table have?

A table has at most one PRIMARY KEY, but it can consist of several columns. It can, however, have many UNIQUE constraints.

CREATE TABLE memberships (
  user_id bigint,
  team_id bigint,
  PRIMARY KEY (user_id, team_id)
);

To be precise: the primary key enforces uniqueness of the combination and no NULLs in its columns. In the example a user can belong to many teams, but only once to a given team.

Pitfall: two columns in a composite key don't mean two primary keys. A foreign key is a different constraint — it makes sure references point at existing data.