If it is alright, I will work on your answer and get back to you tonight.
The concept of applying dispositional theories to relationships is fascinating.
If dispositional theories are correct, we are complex and unique based on the traits, factors and dominant aspects of our personalities. Therefore the integration of those traits and factors into a relationship creates something that is far more complex and unique than what it first appears. For example:
Think of it like breeding dogs. You take a Cocker Spaniel and breed it with a Labrador Retriever, the traits of those dogs (and if you like, personalities) come together in a different pattern than simply adding both dog's measurable traits together. Although the resulting puppy is called a Labradoodle, the puppy is not simply a combination of the two dogs, but a unique breed, with its own character traits in and of itself.
Relationships are like this as well in dispositional theory. I can take your personality, evaluate the measurable factors, such as introversion and extroversion, and then match you to a similar person who shares like traits. But, the combination of both of you is not simply adding up the different traits, but rather how they now interact and influence each other.
So, getting to the heart of your question, your traits can be matched and sorted with others, so that I could expect certain things to happen in a school room for example. The outgoing, boisterous types would congregate together while the reserved, quiet types would do likewise with there own similar personality matches.
So, dispositional theory can, in relative terms, project who aligns with whom and why. It can be used as a basis for dating and potential good matches in marriage. It can be used to infer who might get along at what jobs and who might make the most effective teams.
I hope this helps,