The answer is YES, definitely. In fact, we all have all three doshas in us, just in different distributions. Always remember you have all three, so you can experience imbalances in any of them.
The fact is, most people have just one or two dominant doshas which make up their "prakriti" (personal nature). Some rare people (like me!) have a pretty even blend of all three. That can be quite confusing as it gives us all the positives and all the problems, haha. This chart outlines the characteristics of each dosha, including when they are in balance or out of balance.
If you don't know what your prakriti is, head over here to take a simple survey! If you have two nearly equal doshas in your prakriti, it can be helpful to consider these questions:
1. Which dosha more closely characterizes my body?
2. Which dosha more closely characterizes my mind?
For example, I'm "tri-doshic" but through a lot of contemplation I've come to believe that my doshas distribute themselves in the following way:
Body: My body is more Kapha because I gain weight easily, tend to eat emotionally, and have great endurance.
Mind: My mind is more Pitta because I tend to be very driven, a workaholic, and do have a temper.
My Vata shows up in different ways throughout my life -- I can be very creative, I can have anxiety and difficulty focusing. My sleep is very Vata (interrupted, light). I also have arthritis and really dry skin.
This is just meant to show you that of course you are NOT just one dosha! If you have two or more doshas pretty close to equal, try breaking it down into categories like: your mind, your body, your skin, your sleep, your spirituality, etc. It's fun and can really help you come to more self-understanding!