Can I gain 2 or more cup sizes with breast fat transfer?

An augmentation sounds like what you may need.  A photo would be helpful, but nothing is more important than an in person consultation with a surgeon. 
Assuming that you don't have much droopiness, it can be done with an implant, with fat grafting or with both. I think that all the procedures are excellent and it really depends on each patient's individual needs to determine which is perfect. An implant is tried and tested.  Most plastic surgeons perform this surgery.  In a nice shaped breast most surgeons can produce a nice looking result.  Choosing the right size is the most important step where less than ideal results can occur.
Fat grafting is a great surgery but better suited for patients that have a nice shape to their breast and are not looking to go that much bigger.  You also need to have enough fat to harvest from another part of your body. Not that many surgeons do this procedure.  It is very time consuming and obtaining the best survival of the transferred fat comes with patience and precision.  Not all surgeons can produce consistent results.  Make sure to go to someone that does a lot of fat grafting if you want to make it worth your while.
The final choice is a combination of an implant and fat grafting.  The implant provides most of the size enhancement.  Fat grafting is then done to provide coverage of your breast so that it looks as natural as possible.  It allows for a fuller breast without looking fake.  It also can be used to give a fuller cleavage for patients that have wide set breasts.  This procedure is very advanced. It is really done by very few surgeons.  Even surgeons that do breast surgery as the main focus of their practise may not have experience with this technique.  I love the results that can be obtained with this combo. It is ideal in thin patients that wants to be fuller breasted without the tell-tale signs of an implant.  With that said, it is not required for most patients.
If you have significant breast droopiness, then a lift can be added to the above procedures as needed.
Hope that helps.
Rodger Shortt, Oakville, Ontario Plastic Surgeon 

This is a very difficult question to answer without pictures. Fat can increase the breast size, but you need a good breast envelope to accept fat and enough donor sites to get fat.What would concern me is that you are concerned about having a subtle result which can sometimes happen with fat grafting. I usually consul patients that if they want dramatic results then implants are the better choice for them.Talk to your board certified plastic surgeon.