"On the point of" is a phrase that describes a situation where an event or action is imminent or about to occur. There are several synonyms that can be used in place of this phrase, including "on the brink of," "on the verge of," "nearing completion," "approaching," "about to," "just about," "fit to," "ready to," and "preparing to." All of these phrases can be used interchangeably with "on the point of" to describe a situation that is about to happen or is in the process of happening. It is important to choose the most appropriate synonym depending on the specific context and desired tone of the sentence.