It would be more accurate to say that only one base is visible per system. It is possible to have more than one, but only the most recently built base is visible to other players. You will not lose you base if someone else moves in to the system.
It shouldn’t be possible to claim a base that someone has already claimed. The game doesn’t allow it. I suppose there is a roundabout way to do it by going offline first, but I haven’t heard of anyone trying it.
That being said, we have had a few “incidents” with having bases too close together. When someone moves into your system, it is safest to just move to a different one.