Currently I have 1300cc overfilled saline breast implants, what would be the best way to get into the 3000 or 4000cc range?

As a board certified plastic surgeon from Mayo Clinic with an expertise in cosmetic and reconstructive breast surgery, it cannot be recommended to use any of the FDA approved implants available to over expand to the level you have inquired.  Additionally, there is not an implant available nor is stacking breast implants allowed anymore.  My suggestion is to see a board certified plastic surgeon.  If not in this country, there are additional sizes available in Brazil. 

I do not know any surgeon that would give a patient 3000cc volume in their implants. The implants available in the US can not accommodate those volumes.

Just does not sound like a good idea and there are no implants available, to my knowledge, to get you to that very unusual size request. 

 Usually, the  volumes that you mentioned in your question are achievable (if possible safely) with multiple operations. In my practice, the use of overfilled saline filled implants, accomplishes the goals of most patients who are looking to achieve the “extra large” sizes. Capsulorraphy ('interenal bra")  is necessary in cases where patients have breast implant displacement ( breast implants that drift too far inferiorly or to the sides). You may find the attached link, dedicated to “extra large” breast augmentation outcomes, helpful to you. Best wishes.

To my knowledge, there is not an implant available in the US that will tolerate that much volume. For instance Allergan's largest saline recommends a max fill of 850cc. That can be pushed up to 1300cc as you know but taking it up to 3000cc or 4000cc would almost certainly rupture it or break the fill valve. The largest gel implants are 800cc.

I have specialized in XL breast implants for many years. I have a special arrangement with a couple of breast tissue expander companies as well as custom XL silicone manufacturer and have offices in California/Miami/Nassau/ANGUILLA AND ITALY. Some of my patients have gone well beyond the size that you wish to be! I woiuld suggest you visit my website specifically for XL patients below.I am available for FACETIME/SKYPE/Whatsup video consultations.

Pardon my editorial comment, but this is an absurd request. This would undoubtedly lead to an irreversible deformity with stretching and thinning of your tissues and a deformity for which there would be no good correction. In my opinion, plastic surgeons who would perform such surgeries to the detriment of a patient just because they are asked to do so are not using proper clinical judgment. Perhaps there is a planet somewhere where this would be considered attractive. More to the point, I would not consider this breast augmentation, for the result looks nothing like a human breast. I would classify this as the creation of a cartoon breast, or, more precisely, as breast mutilation.