Obvious disclaimer: I am not a lawyer. Please consult a legal professional for legal advice.
Polyamory is the practice of engaging in multiple loving and consensual relationships at one time. It is legal.
Even though polyamory is legal, however, it is not a legally protected class like being straight or gay. That means you can lose your job for being polyamorous. Courts can use it against you in child custody proceedings.
For more information on the legality of polyamory, I recommend contacting the Polyamory Legal Advocacy Coalition (PLAC).