star trek - Why doesn't the Doctor duplicate himself when he has multiple medical emergencies at the same time?

The Doctor in Star Trek: Voyager is a hologram. Voyager's Sick Bay is loaded with holo-projectors.

The episode "Living Witness" shows that the Doctor regularly makes backup copies of himself. After he gets his Mobile Emitter he is able to transfer his program completely to the device.

In a medical emergency with multiple patients, why doesn't the Doctor ever duplicate himself?

If it's a matter of the ship not having enough processing power, why not transfer his program to the Mobile Emitter and then launch his backup copy from the ship's emitters in Sickbay?

---

In the episode "Concerning Flight", the ship's main computer core is stolen. This cripples weapons, navigation, transporters, and propulsion yet the Doctor continues on in Sickbay unaware as if nothing has happened.

This suggests that the Doctor requires less processing power to sustain his program than the weapon targeting systems, which makes answers suggesting limited processing power seem less likely to be correct.

Answer

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?