There are many synonyms for the phrase "intervened into" that can help add variety and depth to your writing. Some options include "interceded," "inserted," "interjected," "interrupted," and "mediated." These words all convey the general idea of coming between two or more parties or actions, and can be used in a variety of contexts. For example, you might say that a mediator "intervened into" a dispute between two business partners, or that a narrator "inserted" commentary into a story to provide context or commentary. Experimenting with different synonyms for "intervened into" can help you inject more nuance and expressiveness into your writing.