Let's say we have a certain Trill symbiont with a host. What would happen if the symbiont was duplicated under the condition that:
- The host and symbiont were transporter cloned. (2 Jadzia Daxs)
- A person from an alternate timeline with the same symbiont ends up permanently marooned in the prime timeline. (Larry Dax from a timeline where Curzon didn't reinstate Jadzia coexisting with prime Jadzia)
- A past host comes back from the dead with a version of the symbiont a la Spock or Shaxs, or even something similar to Doctor Who's concept of an extraction chamber (Jadzia got bored in Sto'Vo'Kor and decided to climb the Black Mountain, meaning her and Ezri exist simultaneously)
I imagine in all of them, the commission would at least let the duplicate live for the rest of the lifespan of the original host, much like the Federation at large treats transporter clones.
However, what happens when it comes time for the symbiont to be transferred? I can't imagine the commission's ideology would smile upon duplicate experiences under much of the same rationale against re-association: there would be a duplication of experiences rather than the acquiring of new ones.
I think in the first case at least, it is reasonable to assume that they'd begrudgingly transfer both symbionts, as both have the equally valid claim to being the original and randomly killing one is straight-up murder, which I imagine the rest of the Federation would dislike.
They might also do so in the second case, as at least our Larry boy has some different experiences even if some are duplicate with prime Dax.
The third one is where it gets very muddy. The nature of souls in general is a muddy subject - twofold when there are two beings involved. For the sake of argument, we'll say the Jadzia in Ezri's symbiont accessible by Zhian'tara is a "backup" of Jadzia up to her death and that a separate Jadzia Dax went to Sto'Vo'Kor^1^. What then?
1: I make this assumption because a) Ezri doesn't have Jadzia's memories of Sto'Vo'Kor and b) it was the combination of Dax and Jadzia that engaged in Klingon ritual and "just" Jadzia would not be the person that participated. Of course, this starts getting into the more mystical parts of the franchise, and it's probably good they keep it vague even through it makes canon discussion like this a nightmare... a FUN nightmare.
Let's go further, since they already lie about the number of symbionts.
The TSC would take an inspired approach and seek to discover the cloning process so they can scale symbionts to the entire population, and thus finally end the conspiracy.
You get a symbiont, and you get a symbiont, everyone gets a symbiont!
TLDR: The Commission probably wouldn't like it, and the Federation even more so. Even so, there are practical hurtles such as genetic diversity and whether medical knowledge of symbionts is advanced enough to keep a large population healthy and happy.
For one, a fundamental tenet of the ideology of the commission is to protect the well-being of the symbionts, sentient beings, from suffering abuse due to potential competition between Trill over a limited number of symbionts.
If we take the well-being argument further, cloning symbionts has many issues to their well-being. Cloning them would be indignant because it would reduce them to a commodity that every Trill should have rather than a sentient being that chooses a relationship.
Even if the idea got through the commission, I feel like the rest of the Federation might frown on this for those reasons in addition to another: I think there's already a slight bias in Federation culture against the cloning process.
This can be seen in TNG:"Up The Long Ladder" (in addition to revealing that cloning on a large scale has negative implications, Riker is so mad about cloning he murders his own clone and Pulaski's) and TNG:"Second Chances"/LD:"Kayshon, His Eyes Open" (Transporter cloning is seen as a suboptimal circumstance). This suggest culturally, the Federation finds cloning inconvenient at best and a violation at worst. This might be partially negated if the symbionts were to give consent, but it would still feel iffy to most planets
On another note, exact cloning symbiont genomes could have drastic consequences. For one, it would vastly reduce the genetic diversity of the symbionts; this means if there was say, 1 million Daxs with all the same DNA, there's a higher chance that a virus could evolve that's really good at spreading between Daxs, allowing the virus to spread in those Daxs and evolve, probably ultimately killing a lot of symbionts.
The above might be able to be averted if say, you sequenced the DNA of all the (willing) symbionts and generated distinct genome sequences by simulated breeding between symbionts (if they sexually reproduce) or maybe simulating mutations if they reproduce asexually. You could then synthesize the genome and grow a symbiont from it.
Even this better solution might prevent problems, though - what happens when symbionts have genetic defects? With symbionts being so rare, is the medical knowledge of them enough that a large population could be kept healthy?
One thing I left out of my response, and am unsure of, is if duplicate memories would be "louder" when they're brought back.
e.g. if there are 2 Dax symbionts that contribute the memories twice (up until the point they were duplicated), would those memories de-duplicate upon return or would they be more vivid because they were contributed twice?
They could do an episode in this idea too, you got a stew going here 🤙
Some aliens arrive looking for Dax (who remembers them and why they've come) but then the aliens kidnap Dax!
After some science the crew learns that Dax must have diverged in the past and the aliens are seeking the Other Dax.
The crew finds the Other Dax, explains the situation, and cooks up a ruse to free both Dax and Other Dax.
Episode ends on Other Dax's personal log detailing a trip home to the TSC.