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Hello,

So I need your help with the following: which of the sentences is correct?

1. There are a number of factors which, you can't deny, are at play.
2. There are a number of factors which you can't deny (that) they are at play.

Or are they both correct but it is a question of nuance?

To me, it makes sense to omit any prepositions after 'which' seeing as the noun is already mentioned (no. 1), but no. 2 came to me more naturally.

2 is incorrect.
In 1 you could remove the commas. The commas emphasize a parenthetical character of "you can't deny".

[2] There are a number of factors which you can't deny (that) they are at play.

This is ungrammatical because the embedded "play" clause cannot have two subjects, i.e. "which" and "they".

Here is the recipe for creating a sentence with a relative clause.

a) Take two sentences that share a common noun (phrase).
1. There are a number of factors.
2. You can't deny a number of factors are at play.

b) Decide that one of the sentences shall be the subordinate (relative clause), and in that sentence replace the shared noun (phrase) with a relative pronoun.
1. There are a number of factors.
2. You can't deny which are at play.
[Added in the light of #5:] Note that you replace the shared noun with a relative pronoun; you do not replace the shared noun with a pronoun plus the relative pronoun, as seems to have happened in sentence 2 of #1.

c) Move the relative pronoun to the beginning of its sentence.
1. There are a number of factors.
2. which you can't deny are at play.

d) Stick them together.
There are a number of factors which you can't deny are at play.

Note that the element a number of factors is within a subordinate clause within sentence a)2. In some languages, you can't make a relative clause of sentence where, as here, the common noun (phrase) is within a subordinate clause. In English you can, but only if there is no conjunction introducing the subordinate clause. But my sentence a)2. is OK because it does not contain the word that.

se16teddy said:

Here is the recipe for creating a sentence with a relative clause.

a) Take two sentences that share a common noun (phrase).
1. There are a number of factors.
2. You can't deny a number of factors are at play.

b) Decide that one of the sentences shall be the subordinate (relative clause), and in that sentence replace the shared noun (phrase with a relative pronoun.
1. There are a number of factors.
2. You can't deny which are at play.

c) Move the relative pronoun to the beginning of its sentence.
1. There are a number of factors.
2. which you can't deny are at play.

d) Stick them together.
There are a number of factors which you can't deny are at play.

Click to expand...

But that doesn't explain why the OP's example 2. is ungrammatical. The clue is not in the relative clause itself.

[2] There are a number of factors [which you can't deny (that) they are at play].

The relativised element (R) is located within the underlined content clause embedded inside the bracketed relative clause: "You can't deny R are at play".

Thus, R is subject not of the relative clause itself but of the content clause embedded within it. Since the latter already has R as subject, it cannot also have "they" as subject.

Note also that the subordinator "that" is not required to introduce the embedded clause.