Though Tyson doesn’t believe it to be necessarily romantic in nature, or that it is limited to one per person, Tyson does believe in the idea of soulmates.
That two or more people can compliment each other so perfectly as to be considered part of a bigger whole; no lesser when apart, yet in perfect harmony when together. In his mind, the best example of that would be the Moriarty Mirrors.
However, he has seen plenty of other people who compliment each other in that way: inseparable siblings who seem like one being in two bodies, soldiers who fought together as though they had been born to do it, and partners who could have told Tyson that they had been lovers since the earth was formed and Tyson would have believed them.
As for who Tyson would say his soul mates are?
If he asked, Tyson would politely yet firmly refuse to answer. Because to Tyson, the truth is that the two people he’s met who complete his best are now standing on opposite sides of the battlefield from him and from each other: Captain John Watson & Colonel Sebastian Moran.
He’ll freely describe himself and John as simpatico, brothers by all but blood, and yet whilst their temporary peace continues, eventually Tyson knows they will be forced to stand in opposition in the Moriarty Mirrors’ game against Holmes.
The reasons for Sebastian Moran are all to plain to see, as are the reasons it hurts to admit.