[@KatherinWinter]
This would be the Seventh. Using a few Assumptions
1) The first life Was 600 years ago, as most Tsukumogami supposedly need one hundred years to gain life. Even if there were lives before this point they probably don't matter.
2) There are small breaks in-between lives, because do you know how long it takes to reincarnate? Could be instant, could take time I don't know.
3) The current average lifespan of a human is 79 years, as a human in the supernatural world that number maybe lower. 
	So how about this: there were other lives but Ashley doesn't remember them right now, and only thinks there are two. But learns about the others over time as other things happen in the story.