Do soul mates really exist ? Do we have only one soul mate or more ? Well, if we believe in souls, then it makes sense to have soul-mateS; yes, I believe you can have more than one.
First of all, I believe, your soul mate doesn't have to be your life-partner - as against the popular concept. It can be your parents, kids, friends or your life-partner, of course.
Here is what I think makes another soul a 'mate' to your soul - it has a same frequency as yours. As all the particles in the universe vibrate and have their own frequency, so does all souls. We don't see it, feel it or hear it - but these souls are the special particles which make a life and have more than just biological existence. Even animals have souls. So can animals be our soul-mates ? May be. Since we can't talk to them with our language, we can't say for sure; but we do feel it in some cases (dogs, cats etc).
Remember the physics experiment using tuning forks - when we make sound out of two tuning forks, at some point of time the frequencies match and make a harmonious sound. It is like that with souls. When two souls carrying same frequency come near they make 'harmonious sound' together. And that is the reason I believe we can have more than one soul mate in our life time. My assumption is, souls have same frequency at all the time and when two souls go apart physically (not clear about the distance) they can not feel the harmony anymore.
However, when we are not aware of our own soul, we won't be able to feel this harmony created. With all the noise created by our body and its surroundings we may totally miss this near by soul which vibrates at the same frequency. If you are one with your soul (or say can find our inner peace), you may be able to feel your soul mate - may be more than one, in the path of life's journey.
p.s. This is my understanding/theory at this juncture of my life. Frankly, I myself haven't found my inner peace, yet :-)