To quote Ron Pattinson, "Forget what you think you know about parti-gyling. The method employed in the nineteenth and twentieth centuries isn't what you'll find described in home brewing books. " Yes, what the OP describes is what homebrewers have long called parti gyle. But it's not the commercial British practice of that name. Something like the homebrew practice goes back a long way. Before the introduction of sparging, brewers would sometimes run off the wort and proceed to boil and ferment it, "cap" the mash with around 10% fresh malt, reflood the tun, rest, and run off a smaller wort. More than once, maybe. This was never called "parti gyle," and the practice was abandoned after the 18th century, as sparging took hold. The practice of sparging originated in Scotland and was adopted in England from the 1850s. This led eventually to the practice of parti gyle as I describe it, a far more efficient brewing system, which is still in commercial use today. You can look at old brewing books like The London and Country Brewer for variations on the older systems of multiple mashes, each producing a separately hopped and boiled wort, and Ron Pattinson (and later manuals) on "modern" parti gyle methods. Still, the proper distinction is between "parti gyle," literally meaning "split batch," and "multiple mashes." Because I'm being pedantic. And it helps to have a common language for discussion.