I’m looking back at your question and realizing I didn’t really answer.
Frankly, I don’t grind twice anymore, and I don’t intend to do so unless and until I do some emulsified sausage. I just use whatever plate I find appropriate. I’m just doing this as a hobby to please myself and those around me, and I found that I get very little (if any) bang for the buck out of a second grind. I would much rather grind once through my 3mm (1/8") plate than do a second grind
Now, if I had infinite time, a larger grinder, and a dedicated cold room where I could keep all my processing stuff, then I might change my answer. However, I don’t. I gotta tell you, I am very happy with the texture of what I’m cranking out, and I have folks slapping the table when they try it.
That said, I am pretty much sold on the idea of grinding fat no larger than 4.5mm (3/16"). Fat out becomes a much bigger problem at coarser grinds. It’s not that you can’t manage it, but it’s much more difficult. It’s certainly worth the small effort to separate the large chunks of fat in pork butt, beef chuck, and chicken thighs, and then to switch plates (and knives) if you are grinding your leaner bits at coarser than 4.5mm.