In the early 1900s, particularly among the Washington-Franklin heads, the same plate number may be found on different Scott numbers. Why?
Things such as perforation size and watermarks are independent of the printing plate being used. For example, one printing plate could be used to print 10,000 sheets which are perforated 11. The same printing plate could later be used to print 1000 sheets which are perforated 10 because of a decision to change to a different perforation size. These two stamps with different Scott numbers may come from the same printing press.
The same is true with watermarks. As the printing plates were used multiple times over the years to print stamps as needed, the BEP may have moved from unwatermarked, to single line watermark, to double line watermarked paper. The watermark may lead to three different Scott numbers. However, a particular plate number may have been used on two or more of those Scott numbers.