Many times I have had clients ask how many lifetimes they have had. I often give them the opportunity to ask questions of their subconscious mind, though many times their guide may come through or perhaps a group of spirits that help them may come through. Or the same thing may happen during a life between lives session.
The answers we get to this question of how many past lives have I had is usually very general, and may be one something like many or a lot or hundreds. This is not what they are looking for, but it is the most common response.
In response to the question how many past lives can one have, I would say the answer is as many as it takes to learn all the lessons your soul needs to learn. Eventually your soul may get to the point that you no longer need to incarnate in a physical body, then you can stay in the spirit world and help others who are in the physical.