If you think it is better to use Plan-Do-Check-Act-Anticipate, then go ahead. Small adjustment or modification is allowed but you have to agreed that the basic concept is from Plan-Do-Check-Act.
This kind of case common happen like 5S, some company make them to 6S or 7S. No one can say that 5S is wrong and many company still stick to 5S. However, there are still some company are using 6S or 7S, it is fine as long as they think this is better. Again, no matter 6S or 7S, the basic concept is still come from 5S