Can I Increase the Space Between my Breasts with Cosmetic Surgery?

It sounds as if the other surgeons are assuming that you have implants but I didn't get that from your description. Do you have implants? If I am correct and you do not, I am guessing that you are talking about the fullness between the breasts in large chested women.
Generally there is no breast tissue in this location and the fullness is due to extra fat. Using very small cannulae the area can be liposuctioned to reduce the full ness and create a deeper cleavage.

What you are describing is called symmastia. This is a rare complication of breast augmentation when a overly large implant is used and/or over dissection of the pocket where the implant is to be placed medially.

The correction for this is to remove the implants close that space and place smaller implants if any. In certain refractory cases the implant wound have to be removed for 4-6 months and then a repeat surgery performed to place the implants.

 

Hope that answers your question.

The condition of having no division between the breast mounds is called symmastia. It is usually a complication of over dissecting a pocket during breast augmentation or the use of implants that have a diameter that is too large for the chest wall.
It is an extremely difficult complication to correct and most techniques involve using suture to decrease the size of the pocket.
If you have not had previous surgery on your breasts and think that they are just naturally close together (congenital symmastia is extremely rare and I have never seen a case) as long as there is some natural division liposuction techniques can improve the medial contour.
I hope this helps.