In principle, yes. In practice it depends on what special functions or properties you want to assign to a primary key.

In the relational model a key is a minimal superkey - irreducibly unique and not permitting nulls. You can have more than one of those per relation. By convention when there is more than one such key then one of the keys is designated a "primary" one. But that primary designation doesn't make it "special" in any prescribed or fundamental respect. The choice and the difference (if any) between a primary key and a non-primary key is up to you.

Perhaps what you meant to ask is whether SQL's PRIMARY KEY constraint can be used more than once per table. The answer is no. It is an in-built limitation of SQL that PRIMARY KEY can only be used once per table. As Jeff says, you can use a UNIQUE constraint instead and that usually achieves the same things so the restriction on only having one PRIMARY KEY constraint per table isn't necessarily a serious limitation.