Is it permissible for a man to pledge to his wife that he will not marry another woman while he is still married to her?

There is no objection to a man promising his wife that he will not marry another, as this is an relinquishment of his right, not a prohibition of what is permissible. If the wife stipulated this in the marriage contract or before it, then some scholars hold that he is obligated to fulfill it, while the majority view it as merely recommended. If the promise was made by him without any stipulation, then it is recommended for him to fulfill it.