I'm going to argue the point! That design is unique to the (original) Grand Union Canal - they have three staircases of a design that no-one else used.
Going back to Bratch, these, along with the double at Stourbridge, are modifications of the original structure - this form was copied at 14 locks (4 doubles and a treble) on the Monmouth Canal (and acouple of other places on that canal( - the Monmouth Canal ones are not modified, they were built like that, yet the Glamorgan Canal, only a few miles away used conventional staircases. The difference was probably water supply - the Glamorgan had virtually unlimited amounts of the stuff.
The (old) Grand Union design is better, but it is also later - they were built between 1810 and 1814, some 20 years after Fourteen Locks and around 30 years after the Bratch were modified IIRC (1780s or 90s) - Foxton and Watford also come from the other end of the telescope, the objective was to save money and the three staircases have 17 sets of gates and 6 pairs of wing walls between them when the equivalent single locks would have 28 of each. Whilst they wanted to save money they didn't want to waste water, and someone looked at Bratch, did what would now be called a value engineering exercise, and designed out the extra gate.
Edited to add, if your really want a brain teaser look at the side ponds on the two rise at Bascote - they are as per normal single lock, and there are two per lock. It would have taken some coordination to get them used in the right order!