Overrun with is a common phrase used to describe a situation where there are too many of something in a certain place. However, there are several synonyms that can be used in place of this phrase. Some of them include flooded with, swamped with, overwhelmed with, inundated with, besieged with, and inundated by. These synonyms can be used interchangeably with the phrase overrun with to add variety and precision to a sentence. They can be particularly useful when writing or speaking about crowded places, busy regions, or overburdened systems. As a writer, it is always beneficial to have several synonyms at your disposal to enhance your writing skills.