How much fat can be transferred? My doctor told me he can maybe only do 200cc per cheek

Wait for BMI are not great indicators of results or how much fat can be removed.
Fat distribution has by far more important.
Wire pictures alone my guess would be that liposuction of your upper abdomen lower abdomen waist hips and back would yield well over 2 L of fat.
For an impressive BBL I would probably graft 800 to 1400 mL per side
The smallest BBL I've ever performed with 600 mL per side.
I perform these procedures with my patients awake using local Anastasia and mild sedation.
My practiced is devoted exclusively to liposuction and fat transfer procedures.
$5000 it's a fairly low price for a Brazilian but a lot of money to spend if results are not impressive.
Consider a second opinion.
Best,
Mats Hagstrom M.D.

Your photographs suggest that you have far more abundant fat than would be required for only 200 mL per cheek. Buttock augmentation can provide dramatic improvement but I do think you would be capable of transferring and benefiting from a greater volume augmentation. Patients smaller than you having multiple areas harvested in my experience can achieve 600 mL or more readily. Good luck,
Jon A Perlman M.D., FACS
Certified, American Board of Plastic Surgery
ABC-TV/Extreme Makeover Plastic Surgeon
Beverly Hills, California