@nick raises some great points. It is lawful for a married man to marry a second wife, but already having a wife is a complication that the single man simply does not have.
Already having a wife is one of a thousand possible complications that would practically impact marriage ability.
Here are a few other practical complications to potential marriage.
A man with children need to think about how a particular marriage will affect his children. He is free to marry as he chooses, but marrying a woman who hates his children (or that his children hate) is very risky.
A man heading off to war is free to marry, but should consider whether that is the right time for marriage.
A man with serious health problems, or serious financial problems is completely free to marry, but these issues are still factors.
The man adding an additional wife should very carefully consider how the possible additional woman will impact his existing wife and family.
Again, he is able to take a second wife, but needs to be more cautious than a young single man.