It is certainly possible, I seem to have increased my BMR in the last decade by exercising harder, longer and more frequently, while eating a lot more. My body seems to have adjusted to that by dramatically increasing the BMR.
I now eat about 3800 Kcal per day while the BMR formula says that my BMR should be about 1700 Kcal/day. There is no doubt about how much I eat, because I weigh and measure all the food I eat every day. I need to do that because I eat huge amounts of food for someone my size; without measuring I would prepare too much or too little food.
I also know that it is the the BMR that is extremely high and not just the total metabolic rate, because on vacation when I typically exercise a lot less, I typically lose some weight. While I then do eat a little less, the difference is only a few hundred Kcal/day; dinner in the hotel is still about 1800 Kcal, which is more than what according to the BMR formula my entire energy intake for the whole day should be.
One could argue that I could have some problem with digesting food, but I have all the signs of someone with a fast metabolism. E.g. I can tolerate extremely cold conditions quite well.
Wim Hof has developed another method, not really aimed at increasing the BMR, but it does have that effect too. By taking daily cold showers and certain meditation exercises, you can increase your BMR at will. E.g. Wim Hof has broken the ice endurance record, during his record attempt he doesn't shiver, his heart rate hardly increases. So, the extra heat produced by his body is not due to additional muscle contractions:
Mr Hof said he can endure sub-zero temperatures as he has the ability to 'turn his own thermostat up' by using his mind.