No, they don’t get a say in what assets go to which people or organizations. Their job is to bequeath assets based on the testator’s wishes, as well as pay debts that the estate owes. There is, however, an exception to this rule. If the testator’s wishes are unclear in the will, then it may be up to the executor to decide who gets what. For example, if their wishes say that the house must be sold and the proceeds must be given to charity, it may be up to the person running the estate to choose which organization to donate to.