Is it permissible to have intercourse with one's wife multiple times in a single night and perform ghusl (ritual bath) only once at the end, or is it obligatory to perform ghusl after each act of intercourse?

There is no objection to a man having intercourse with his wife multiple times without performing ghusl (ritual bath). It is, however, recommended for him to perform wudu' (ablution) between the two acts of intercourse, based on the Prophet's (peace be upon him) saying: "If one of you comes to his wife, and then wishes to return, let him perform wudu'." The wudu' is recommended, not obligatory, as indicated by the Prophet's (peace be upon him) saying: "For it is more energizing for the return." This is further supported by what Aisha (may Allah be pleased with her) narrated, that the Prophet (peace be upon him) would have intercourse and then return without performing wudu'.