§1. When he receives baptism in the Catholic Church, a non-baptized man who has several non-baptized wives at the same time can retain one of them after the others have been dismissed, if it is hard for him to remain with the first one. The same is valid for a non-baptized woman who has several non-baptized husbands at the same time.
§2. In the cases mentioned in §1, marriage must be contracted in legitimate form after baptism has been received, and the prescripts about mixed marriages, if necessary, and other matters required by the law are to be observed.
§3. Keeping in mind the moral, social, and economic conditions of places and of persons, the local ordinary is to take care that the needs of the first wife and the others dismissed are sufficiently provided for according to the norms of justice, Christian charity, and natural equity.
Source: Code of Canon Law (Vatican.va)