There are allusions to the fact that there may be more like River Tam, but AFAIK none were introduced.
Also, she is definitely the most powerful and least crazy of the psychics that I can tell from the way they talked about her, possibly the only one left alive.
The first 10 - 20 minutes of Serenity are probably the best place to look for these clues.
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Remember, they were keeping all of the psychics in a top secret facility, and remember what it took to get River out.
There probably aren't too many of them left, but there definitely were other psychics in the 'verse.
I bet some of them would have turned up if the series kept going on, most likely as weapons, as it appeared that River was intended for.
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I think, though this wouldn't be considered canon even if true, we lost a lot in Firefly when it the series was canceled.
When you look at Whedon's body of work, he plants story seeds that develop over years (think of Dawn in Buffy, she was alluded to years before she came on the scene and
Willow going evil -- the seeds for that were planted in season 2 when she resouled Angel).
So, I think Whedon had planned to develop this over several years, but the series was cancelled and a lot of what we would've seen over five or six seasons on the series was compressed into the movie.
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There are girls who have been subject to same experiments as River In Serenity - Leaves on the Wind 1 , our heroes need to break into the facility where River was held.
Without spoiling too much, River definitely isn't the only one, although the good doctor that made her states that she had a unique mind.
We don't actually see any other displays of psychic powers, but the other subjects are described as complete (as opposed to River), and they're definitely on par with River when it comes to fights.
1 Written by Zack Whedon, produced by Joss Whedon, thus
canon
Sorry for the quality of the last one
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The only potentially canonical source that directly states the possibility of more psychics is the roleplaying book Serenity , where Psychic is a trait any character can pick up.
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A few sub-answers: A possible answer lies in the context of River's nightmare in the opening scene of the BDM.
When I first saw that scene, I assumed that we were seeing a nightmare set in the school.
If that's the case, then those other kids are in the same training program, and presumably have many of the same qualifications.
When Simon recounts to the crew the coded message that River wrote to him, his phrasing is "They're hurting us", with the plural pronoun.
However, given that Simon lies about other details in this same scene (specifically, concealing that it was in fact he who broke River out), the veracity of his account is nonverifiable.
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Since it's introduced quite early in the series, I was surprised that no further psychics turned up in Serenity (if there's one there's two).  Are there any other instances of psychics in the Firefly universe (or 'verse) in the rest of the canon?
Other than River Tam, are there any other Psychics in the Firefly 'verse?
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There have been allusions to other psychics in the firefly universe and some consider that there are definitely more psychics. However, none of them have been introduced. Although you don't actually see any other displays of psychic powers, the other subjects are described as  complete  (as opposed to River), and they are definitely on par with River when it comes to fights. It would seem there probably are other psychics in the Firefly universe although they are only alluded to rather than seen.
It would seem there probably are other psychics in the Firefly universe although they are only alluded to rather than seen.