grammar - How can verb て become an adverb?

I found a sentence

医者が「大丈夫ですか」と重ねて尋ねた。

with translation

The doctor repeatedly asked "Is it OK?".

As far as I know

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  The concatenation of て verb represents several actions which are done one after another. For example, 持って行く means "bring" followed by "go".

  
  
  


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  Changing the last い in い adjective　to く makes it an adverb. For example, 早く来てくださいね.

  
  


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  Or adding に after な adjective to makes it as an adverb. For example, 簡単に説明してください.

  
  

How can 重ねて (to repeat) followed by 尋ねた (asked) become "repeatedly asked" ? Is there any grammar I am missing here?

Answer

The concatenation of て verb represents several actions which are done one after another. For example, 持って行く means "bring" followed by "go".

No, this is not always true. Te-form can combine two verbs like the English conjunction "and", but it does not necessarily mean the two actions happen one after another. For example, te-form can denote a method. 歩いて学校に行く means "go to school on foot" rather than "walk, and then go to school". Te-form is also used to express two things happening simultaneously. 立って話をする usually means "talk while standing" rather than "stand up, and then talk".

持って行く means "to have/hold" and "to go" occurring at the same time, hence the combined meaning of "to bring". (To be clear, 持つ alone does not mean "bring"!) In general, these subsidiary verbs do not represent two actions happening one after the other.

Now, the primary meaning of 重ねる is to pile something up, but the verb itself can mean to repeat. Here's デジタル大辞泉's corresponding definition:

２ ある物事に、さらにそれと同類の物事を加える。また、同じことを何度も繰り返す。「悪事を―・ねる」「努力を―・ねる」「年月を―・ねる」

The meaning of 重ねて尋ねる can be understood along the lines of 歩いて学校に行く and 立って話をする above. Here, the first verb before て describes how the second verb is done, in which situation the second verb is done, etc. That's why 重ねて尋ねる means "ask in a repetitive manner" rather than "repeat, and then ask".