There are a number of synonyms for the term "more half-yearly", which refers to something that occurs more frequently than twice a year. Some possible alternatives include "quarterly" (which happens four times a year), "bimonthly" (which happens every two months), "monthly" (which happens twelve times a year), or "biweekly" (which happens every two weeks). These different terms could be used depending on the level of frequency desired, with some businesses or organizations opting for a bimonthly meeting schedule, for instance, while others might hold monthly or quarterly gatherings. Ultimately, the choice of synonym will depend on the specific context and needs of the situation at hand.