Polygamy
What becomes of the other wives if a man is baptised?
The predicament of a man who, desiring to convert to the Gospel, is obliged to repudiate one or more wives with whom he has shared years of conjugal life, is understandable. However polygamy is not in accord with the moral law." [Conjugal] communion is radically contradicted by polygamy; this, in fact, directly negates the plan of God which was revealed from the beginning, because it is contrary to the equal personal dignity of men and women who in matrimony give themselves with a love that is total and therefore unique and exclusive." FC 19; cf. GS 47 # 2. The Christian who has previously lived in polygamy has a grave duty in justice to honor the obligations contracted in regard to his former wives and his children.
§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.