What are the criteria in Islam which permit a man to marry more than one wife?

The fundamental criteria for Polygyny are that of justice, being able to maintain justice between the wives, and being capable of maintaining the wife. If a wife wishes to maintain herself, that may be removed as a requirement, but as a fundamental requirement it is there, that he should be capable of maintaining those whom he marries.  So if he is unable to maintain more than one wife, then he is not allowed to marry more than one wife, if he cannot deal justly with them, then he is also not allowed to marry more than one wife, as this is a fundamental condition. Other than that, in time, people have tried, in an attempt to make the plural marriage allowance in Islam seem more reasonable, they have said, that a man can only marry more than one wife, if he doesn't have any children by his first wife, but this is not a principle and it is not a requirement and as I said, humans’ welfare is a fundamental principle which dictates the allowance for plural marriages and it has nothing to do with having children or not having children. It may seem quite reasonable, that if a person cannot have children by his first wife, and it is a desire of each and every one of us to have children, so in that circumstance he can also have another wife, but it is not a condition.