The Pilates Footwork is comprised of four positions in a specific order. Two separate films exist of Joseph Pilates teaching the footwork. In both films the order is the same. In one of the films, close ups are made after the full body exercises are displayed. The order is this: Pilates V, arches with soft feet, heels on bar in dorsiflexion, then on metatarsals in parallel with only one lower lift of the heels between each extension of the legs.
Variation of the footwork is a gross error of judgment and presumption on the part of the teacher. Sure, you might choose different positions or order to the footwork, for whimsy or reason, but in the end, the target is the footwork of Joseph Pilates.
Joseph Pilates never explained much about the "why" of the footwork. But when you consider Pilates as an idea, as Michael Miller Pilates professes that it is, the reason for the position and sequence of the Footwork exercises becomes self-evident. Subscribers can click here for explanation.