If one's goal is fat loss, it is counterproductive to expand protein intake. That reduces muscle loss somewhat but with significantly less fat loss for a given activity level.
As much as half of one's protein intake (Pearson & Shaw claimed average 47%) undergoes gluconeogenesis on the first pass through the liver. The proportion differs for different amino acids with glutamine being one of the highest. It increases when carbs are restricted but does decrease significantly when protein is restricted to avoid cannibalizing the most rapidly available amino-acid stores in skeletal muscle.
The typical ketogenic low-carb diet allows something less than 100 grams of carbohydrate in addition to some reasonable amount of protein. Increase the protein intake by 100 grams and one's carb allowance drops below 50 grams. Increase the protein intake by 200 grams and the carbohydrate allowance drops below 0 grams.
Children with epilepsy are sometimes prescribed ketogenic diets. Even with much of their fat intake in the form of medium-chain triglycerides which preferentially convert to ketones, these children can drop out of ketosis due to excess protein. They count 100% of protein intake against carbs and aim for 4 calories from fat for each calorie from combined protein and carbohydrate.
One must also count free-form amino acids, dipeptides like creatine, carnitine and carnosine and any other peptide supplements into one's protein intake.
Most low-carb diets are really not ketogenic due to excess protein intake and do not reduce body fat as effectively as a true ketogenic diet.