I always had good luck with a big adjustable wrench to remove even the tightest BB fixed cup, type with the two flats on it. Trick is preparation and patience.
It is always tempting to attack the fixed cup with a tool like an adjustable wtrench like an ape, but the best thing to do is to take your time and first stabilize the frame of the bike by laying it down on it's side on the ground, and making sure that it will not see-saw or move around on you when you apply force on it. I always just bunch up a big old blanket or quilt on a carpetted floor and lay the frame on it. Careful adjustment and tightening of the large adjustable wrench (Ideally the size with a handle over a foot long) will have the same results as doing it with a proprietary fixed cup wrench. Just do it slowly and easy with constant checking on the adjustment of the wrench so you avoid having it pop off on you (also push down on the head of the wrench against the BB face while you are applying torque. It's when the wrenches pop off on you and you ruin the flats on the fixed cup that the real trouble starts.
BTW, it will be good if you also pre-treat the fixed cup by spraying some penetrant lubricant on it from inside the BB shell. Liquid Wrench, PB blaster or Freeze-Off should work nicely.

Good luck, and remember to take your time and it should work out.
Haven't had a fixed cup beat me yet in over 20 years of wrenching on bikes.

Chombi