Levin said there are various centers around the world that have the capability to pull off a face transplant; the technical particulars of the surgery are becoming more widely understood.
But he also said that how doctors ensure that the patients' bodies do not reject the transplanted tissue after the operation is crucial.
Case in point is face transplant recipient Dinoire, who has already suffered several bouts of what doctors call "subacute rejection" -- complications that result from the patient's immune system attempting to reject the transplant.
"The patients are far from out of the woods after the surgery is over," Levin said.
In order to prevent this rejection from occurring, patients must take a cocktail of drugs designed to suppress their immune systems. But Costantino said the use of these drugs restricts certain patients from consideration for these procedures.
In particular, cancer patients who have been disfigured by the disease would not be able to take advantage of this option because of the necessity for immunosuppressive therapy.
"If the patient had a cancer, it's really not appropriate," he said. "We're not really anywhere near doing this in cancer patients because of the immunosuppressive effect on the cancer maybe coming back."
Other challenges come naturally in dealing with the face -- a remarkably complex part of the body that is the site of dozens of delicate muscles and nerves.
Costantino said eyelids are a particularly difficult area where transplant is concerned.
"That's why you're seeing these face transplants focus on nose, mouth and chin," he said. "Right now I think that the partial face transplant really is the face transplant."
And then there is the question of public acceptance. While people may be more accustomed to the idea of a face transplant than they were in 2005, many would still balk at the idea of donating their own face for transplant.
As more face transplants are performed, this hesitance could even spell a problem for organ donation in general. Levin said that the public could fall prey to the misconception that becoming an organ donor would mean that the face is also up for grabs.
"If the public perceives that this is a possibility, they may balk and say that they don't want to donate their organs at all," Levin said. "The last thing that we want to do is make organs harder to procure."
Despite the challenges facing this procedure, surgeons are hopeful that face transplants will be beneficial to many patients once these issues are solved.
The applications of this procedure will "absolutely explode exponentially," Levin said. "This is what all of us involved with the ravages of cancer, traumatic accidents and congenital diseases are all waiting for."
And these surgeons may not have to wait much longer. Doctors in Britain and the United States are currently working toward their countries' first face transplants.
"There are many complex issues here, but there is an entire cadre of surgeons such as myself who want to see this go forward," Levin said. "I think things are advancing at a pretty rapid clip, and I hope that in the next couple of years we'll see some major breakthroughs.
"I truly believe that when the scientific aspects of transplant immunology are solved, this will become a clinical reality," he said.