In an article from the Associated Press, a Vatican official defends the church's stance that marriage is only between a man and a woman and should not be open to homosexuals by asking why we don't go ahead and allow polygamy.
What's the Objectivist answer? Should consensual polygamy be allowed?
Objectivism may have a lot to say about the nature of love and sex, but all of that is actually irrelevant in this context, because what's important here is Objectivism's view of the role of government.
Objectivism holds that the role of government is to uphold individual rights -- to bar physical force from human relationships.
As long a relationship (or group of relationships) is fully consensual, according to Objectivism, government shall not interfere.
If a group of people are behaving peacefully, no matter how distasteful their behavior may be to other people, including Objectivists, the government shall protect their right to do as they wish.
No-one has a right not to be offended by the behavior of others. Government is not and shall not be an enforcer of good taste or good judgment.
The above regards the behavior of polygamy. Of course, though, the terms "marriage" and "spouse" have legal meanings, and so to simply introduce polygamy as a form of marriage would be to subvert legal precedent. Polygamy would have to be considered a new form of contract.