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To my understanding, `誰｛だれ｝が猫｛ねこ｝が好き｛すき｝？` is a valid sentence in Japanese.
What exactly is happening here with the two が particles? Is it really the case
that `好き` can take two subjects? Or is it that there is some hidden
information that we never usually say, such as `誰が猫が好き（と思う｛おもう｝）？` so that `誰`
goes with `思う` and `猫` goes with `好き`?

Similarly, what is going on with the sentence `誰が黒い猫がいますか？`?
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particles
Double が particles
You can have multiple occurrences of が in a sentence, but that does not mean
that there are multiple subjects of the sentence.

This has been discussed in academic papers on Japanese, and there doesn't seem
to be consensus on how to describe the phenomenon in linguistic terms. For
example, Tsujimura (1996) suggests two 'tests' for identifying the true
subject of a sentence: reflexivization (use of specific words like 自分), and
subject honorification (use of verb forms like お～になる). Noguchi (2018) points
to other possibilities such as the use of "body-part nominals" like 身を～.
Jorden (1987) talks about "affective" predicates which allow for multiple uses
of が. Also, things like word order are not a reliable way to identify the
subject.

In most cases, a native speaker would intuitively understand what the intended
subject is. But for a learner, it is not always so easy. When it is possible
to identify the subject using linguistic tests such as those described above,
that is probably the best way. When that is not possible, you will have to try
to understand the content and context of the sentence since there doesn't
appear to be any watertight rules for treating sentences which contain
multiple instances of が.

**Sources:**

  * _Tsujimura, N. (1996). An Introduction to Japanese Linguistics (3rd ed.). Oxford: John Benjamins Publishing Company._
  * _Noguchi, T. (2018). Two Types of Reflexivization in Japanese. Japanese/Korean Linguistics, 25, 1–11._
  * _Jorden, E. H., & Noda, M. (1987). Japanese: The Spoken Language. Part 1. Yale: Yale University Press._
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> To my understanding, 「誰{だれ}が猫{ねこ}が好{す}き？」 is a valid sentence in Japanese.

It is only valid in highly informal/colloquial conversation even though this
has nothing to do with the use of the double-が. It has to do with the lack of
words at the end following the 「好き」.

As is, the above phrase can mean at least two completely different things and
those are:

**1) "Who likes cats?"**

**2) "Who did you (just) say likes cats?"**

For the first meaning, it would be more natural to say 「誰が猫が好きなの？」 or even
「猫が好きなのは誰（ですか）。」

The second meaning/usage works like this.

Person A: 「[Personal Name] + さん/ちゃん/くん + って猫が好きなんだって。」

Person B was unable to catch the name so s/he replies:

Person B: 「誰が猫が好き？」 ("Who did you just say likes cats?")

B could have replied with a longer sentence such as:

  * 「誰が猫が好きだって？」

  * 「（今{いま}）誰が猫が好きだって言った？」

Hope you are following all this.

For either meaning/usage, the double-が is 100% justifiable.

The 「が」 in 「[Object] + **が** + 好き」 ("to be fond of [Object]") is simply the
only natural particle choice, except for the contrastive 「は」 used when saying
"to be fond of X but not Y", which would be 「Ｘ **は** 好きだが **Ｙ** は好きではない」.

(For the nit-picky, 「の」 is also possible when forming an **adjective phrase**
with 「好き」 as in 「ボク **の** 好きな食{た}べものはピザです。」)

In addition, the 「が」 is the only proper subject-marker when a question word
（だれ、どこ、なに、いつ, etc.） is used as the subject of the sentence. Again, the
contrastive 「は」 is the exception.

This might sound simplistic, but if both 「誰が好き」 and 「猫が好き」 are correct and
natural-sounding, which they are, then the combination of the two 「誰が猫が好き」
will also be correct and natural-sounding.

> Similarly, what is going on with the sentence 「誰が黒{くろ}い猫がいますか？」?

That sounds highly informal, too, but still 'valid'. I just cannot say native
speakers do not say that. They do and that is the only reason that I know what
it means. It means " **Who has/keeps a black cat (as a pet)?** "

Again, it would be more natural and unambiguous to say:

  * 「誰が黒い猫を飼{か}っていますか。」 or

  * 「黒い猫を飼っているのは誰ですか。」
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