Firstly, it is very rare to have identical triplets due to the way that the cells split, they split 2, 4, 8, 16 etc....Each cell splits in to 2 each time. The conjoined aspect happens when the cells split, the glue holding them together actually comes apart a little, not fully. Depending on where the cells are partially joined depends on where the twins are 'attached'. So I should imagine Scientifically it's possible, although imagine how rare triplets are, how rare conjoined twins are....the partial separation of the cells would have to happen twice.
"There has been only one confirmed case of conjoined triplets. Conjoined siblings occur only in monozygotic multiples. Triplets are most often what is commonly referred to as "a pair and a spare" meaning two are identical and one is fraternal. Two eggs are fertilized and one splits. Identical triplets are very rare, occurring in about 1/200,000 births. They are always the same sex. I am the grandmother of identical triplet girls born in 1998. They suffered from Twin to Twin Transfusion syndrome with one donor baby and two recipient babies. Their birth weights at 31/6 were between 1190gr-1759gr. At 10 years they are healthy, normal girls."
"Can conjoined triplets (or other higher multiples) exist? Dr. Rowena Spencer's 2003 book Conjoined Twins: Developmental Malformations and Clinical Implications discusses several cases of supposed conjoined triplets and quadruplets, most of which consist of one autosite with a number of parasites or acardiac twins (see above). However, a 2004 article in The American Journal of Obstetrics and Gynecology describes a case of parapagus dicephalus dibrachius dipus twins with triplet joined to the shared sternum, in the manner of xiphopagus twins. All three fetuses were well-formed and had approximately normal heads and extremities. This article provides conclusive proof that conjoined triplets, although extremely uncommon, CAN OCCUR"