In "Basics: Part 1" when Voyager fights multiple Kazon factions, they created multiple holographic fighter ships to distribute the shots from the Kazon ships so that Voyager came under less fire. When they first initialise these holographic ships, the Doctor appears in space stating:

> TORRES [OC]: Doctor, are you there? Are you all right? 

> EMH: I told you we should have run one last systems check.

Indicating that these holographic ships run under the same computer program as the Doctor. This proves that it is, in fact, possible for there to be multiple copies of a hologram running simultaneously. I assume that this never happens in the show for the same reason that transporters cannot create copies, or replicators cannot be used for cloning, yet they can be used to create organs.

There are tons of contradictions like this in the _Star Trek_ series. Stuff like that is inevitable with science fiction, although _Star Trek_ does a very good job at being scientifically accurate as often as possible (where the narrative allows anyways). In one episode of _Star Trek_ (TNG I believe) they used a transporter to get rid of a virus in one of the crew's body using a backup from the transporter logs. If this was truly possible, don't you think they would have done this more often? Such as healing injured crew members, or even bringing them back from the dead?