Increased rapidly

Usage examples of escalated.

But the most ominous part of the message was that the world situation had escalated to a conventional shooting war, with employment of nuclear arms anticipated.

Or had it come down to threats between the two superpowers which eventually escalated to a missile exchange?

With a malicious grin, but barely a hint of effort, Sartol escalated his assault, drawing a brighter, angrier flame from the vast crystal.

Then, when she had learned that he was smart, the sort who did what he said he would do, and had enormous strength of character, her positive first impression had escalated to another level.