I know from this question that a death note could only belong to one person at a time, but I was wondering if the opposite was true--that one person could own multiple death notes. Could, say, that person go around killing the owners of death notes and stealing them in an effort to do something like own all of the death notes?
Apparently yes, there are rules about how the Death Note works if someone has more than 1. These rules are stated in How to Use: XXIII
Whenever an individual with ownership of more than two Death Notes loses possession to one of the Death Notes, he will not be able to recognize that Death Note's god of death's appearance or voice anymore. The god of death himself will leave, but all the memory involving that Death Note will remain as long as he maintains ownership of at least one other Death Note.
And in How to Use: XXXII
If someone possesses more than one Death Note, by visualizing the victim, then writing down the name in one of the Death Notes and the cause of death in the other, it will take effect. The order however, is unimportant, if you write down the cause of death in one Death Note and afterwards, write the name in the other, it will take effect.
We also see Light owning 2 Death Notes in Episode 25 - Silence and in Chapter 58 - Feelings Within. while the scenes play out differently in both Light becomes the owner of Rem's Death Note after she has died. in Death Note: The Last Name we however never see this as Rem destroys her Death Note in the equivalent scene.
There is however a limit of 6 Death Notes that a single persona can own. This is because only 6 death Notes can be active as it is stated in How to Use: LII, Point 1
In the event that there are more than 6 Death Notes in the human world, only the first 6 Death Notes that have been delivered to humans will have effect.
One can assume "ownership" will not work unless the Death Note is active, so the 7th Death Note can probably be passed around. But when one of the currently active 6 is removed (destroyed or taken back to the Shinigami Realm), the person currently holding the 7th will become the owner.