That sounds good in theory but didn’t work for me. I didn’t take any supplemental protein and I was still having trouble going into ketosis (according to test strips). I finally had to cut out pretty much all meat for a few days to see if I could finally go into keto. I did go into ketosis but I was miserable and quit after a couple of days.
It’s called keto flu and only lasts a handful of days. If you’d kept going another day or two, you’d probably felt better than you did before you started keto. If you ever try it again - remember to eat high fat meats (beef) rather than high protein (chicken) or at least add a bunch of high fat items to it (sour cream, butter, high fat cheeses, etc).