Advanced 5/3/1 in the Beyond 5/3/1 book is pretty much what you are describing. With the advanced template I had great success increasing my 1 rep maxes. This was mostly because I was getting really good “practice” with singles on the 5x1 weeks as well as building technique on the previous weeks. If I feel it was going to be “one of those days” I would attempt a new PR (5x1 week) on a certain lift but this was always on the week before a deload. With that said, I always made sure to reset my training maxes when going back to the original setup of setting rep PR’s or 5’s Pro. Going back to setting rep PR’s is a bit different for me than doing multiple sets of 5, 3, or 1’s.
Having read all of the books (except for the new one) and running 5/3/1 for several years, I got a pretty decent understanding of what “templates” work for me and what I want to achieve but the 5/3/1 principles have always remained the same. Too many folks have tried to make 5/3/1 “Rocket Surgery” when in reality all of the answers are pretty much right in front of them in print and are pretty simple. I’m looking forward to getting the new book and getting an even better understanding of his new programming mindset. He’s put a ton on these forums for free but want to read the method behind the madness!