I think you mean Supplemental. It might seem like I am splitting hairs, but in the context of the program I think the distinction is warranted to make sure we are on the same page.
Feel free to disagree, but I feel like all of the 5x5/3/1 variants are pretty volume focused. Even Rhodes (which I have yet admittedly I have yet to run) your still gonna get some appreciable barbell reps in if your TM is set properly you hit the first two sets and you push that third set as hard as you should.
I don’t think its a question of “in bounds” or “out of bounds”. I think its more of what the “best practices” are. Since in that section of the book Jim outlines how to do FSL or BBS, I would say those two are probably the most effective way to supplement your workload with 5x5/3/1. Also the supplemental pattern you are describing isn’t correct. Your supposed to pair an upper body lift with lower body lift every session, not just change from deadlift to squat, or bench press to press.
You are of course free to try whatever you want, but I don’t think anyone is going to sign off on it. You are probably on your own on that one. My understanding of the best way to run BBB is with 5;s pro, or capping your PR sets at minimum reps, and putting all your energy into the 5x10. So maybe capping all your Rhodes work at 5 reps would do the trick as long as your not taking anything away from BBB work. I say just do BBS instead, I think it works better as its easier to maintain form in the later sets and your less likely to miss reps than on BBB.
Then why not flip one more page and run Portal’s 5x5/3/1. That’s actually right in line with this. It doesn’t have the PR sets in the Leader but its still pretty challenging. The toughest 5/3/1 template I have ever run for sure, but well worth it.