So, here is a good start -- several recognized experts comment on their thoughts on the tri-color possibility:
Joan Gordon
"According to many present-day writers Yorkshires were the result of
a number of breeds being bred together to produce the desired points. How anyone could believe, or even imagine, these early fanciers would have bred from a Dandie Dinmont, a breed with an uneven top line; a Maltese, a totally white breed lacking any blue or tan markings or from a smooth coated Manchester Terrier (originally a smooth coated Old English Terrier) is not being realistic. "http://www.ytca.org/history.html
Malcolm Willis' "Genetics of the Dog"
The genetic makeup for the Yorkshire Terrier is:
asasBBCCDDEEGGmmSStt
S Self colour to totally pigmented surface si Irish spotting involving a few definite areas of white sp Piebald spotting sw Extreme-white piebald
Most breeds without white markings are SS but from time to time markings do appear and in general appear on toes, chest or muzzle. These marks can be present at birth and are lost during infancy. The ones that persist are not other s alleles but to minus modifiers at the S allele and will be limited to those minute amounts in those locations.
Irish spotting is also limited to certain areas of the body as the dominant S is, ruling out either gene in the makeup of Parti Yorkie Tri Colors or Biewers. Limited to forehead, chest, belly, feet and tail tip.
Piebald shows much larger amounts of white on the dogs then the Irish spotting gene.
Extreme-white piebald is seen in those breeds which are white in color. As a result of this double carrier of swsw all other colors can be suppressed. (From Malcolm Willis "Genetics of the Dog")
So in essense, to have the white markings that are on the so called Parti Yorkie Tri Color or Biewer dogs, another breed had to have been in the mixture at some point. Since no one wants to admit this and in all honesty, it could be back far enough that no one is living any longer to admit to it, but unlikely that it is not much closer up. After some study of the current Biewer situation, which is somewhat the same situation, I've found they have both the Piebald gene and the Extreme-White Piebald gene. Some of the Biewer's are going almost solid white, which gives and indication of a couple different breeds.
Malcolm Willis' "Genetics of the Dog" When you read the genetic study of the Maltese, they have the Extreme-White Piebald gene.
Even though the genetic studies were not conducted on Shih Tzu, it is quite apparent that they are carrying the Piebald gene. Either or both could figure into the equation. The ones going white are heavy on the Extreme-White Piebald and the ones keeping color on the backs are of the Piebald inheritance. Either way, the mix wherever it happend, by accident or plan, this is NO longer a purebred Yorkshire Terrier.
In over 30 years of being involved in the sport and many Yorkshire Terrier champions, I have not had a Yorkshire Terrier with white. I find it interesting that the only ones coming up are the ones not bred by show exhibitors. A show exhibitor was getting them and had enough sense to realize there was more behind her breeding then just the Yorkshire Terrier and somebody had obviously done a breeding that was not pure Yorkshire Terrier. Otherwise the show exhibitors are not getting these white colored dogs."
Top Parti Yorkies Genetics Party Color and Biewer