The data is there but only with respect to increase in strength and total strength.
WNDTP | Kunkel, Racculia, and Wisneski
What we know is that statements like "200 lbs on your squat depending on how young, healthy, and male you are" exist. BW measures aren't used because the program is about getting bigger and stronger. They will tell the OP to gain (and continue to gain) weight. Gaining weight will make you stronger... it also will (eventually) reduce your bodyweight ratios.
You will note the OP asked if his thinking was the problem. I pointed out how the books, articles, etc tend to think about it... which is "it runs out when it runs out". There are other training methods and programs after linear.
Should the OP be able to squat 3 plates with enough effort and training?... assuming he has okay genetics and medical history then sure.
Will the OP be able to squat 3 plates before is LP runs out?... no idea.