If I'm not mistaken, another is a contraction of an other , but since an/a mean singular, saying many another would seem incorrect.
english.stackexchange.com/users/1923/JohnoBoy
The Free Dictionary as well as Merriam-Webster say that "many a/another" expresses "each of a large indefinite number".
"many a man" "many another day will come" In German it would be translated as "so manch", "manch ein".
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Compare 1M and 135M, I don't think "like many another" is a standard phrase.
I haven't seen it before until now in this question, and I don't think it's correct either.
english.stackexchange.com/users/2013/Gan
"Many a" is an idiom, a fossilised remnant of a construction which is no longer productive in English.
I would say it has a rather archaic flavour itself, and would not be used in formal contexts.
"Many another" is an extension of this, and feels odd to me.
english.stackexchange.com/users/547/Colin Fine
Undeniably the construction is less common than it was , but it's still perfectly standard English... ...which includes 8300
written instances in Google Books from the 21st century.
Note that it's the equivalent of "
Like many others " , not "Like many other" , unless followed by a plural noun (where "Like many other children" equates to "Like many another child " ).
english.stackexchange.com/users/2637/FumbleFingers
The phrase 'like many another' is perfectly legitimate, though possibly slightly old fashioned (like me, but I've used the phrase on many another occasion, though not in EL&U answers as it happens).
The comparison is with a singular object, which can be stated explicitly or omitted (implied).
The word 'child' (or 'student') is optional in the following examples; the sentences are both grammatically correct.
Like many another in his class, John is thirteen years old.
Like many another child in his class, John is thirteen years old.
The phrase 'like many other' requires an object, which must be plural and explicit.
Omitting 'children' leaves a non-grammatical sentence.
Like many other children in his class, John is thirteen years old.
The phrase 'like many others' uses an implicit plural object (which must be omitted).
Although the comparison is with the other children, you cannot include 'children' in the comparison while you keep 'others'.
Like many others in his class, John is thirteen years old.
You could also write any of the following, each of which uses only one of 'many' or 'other': Like many in his class
, John is thirteen years old.
Like many children in his class, John is thirteen years old.
Like others in his class, John is thirteen years old.
Like other children in his class, John is thirteen years old.
Writing the following has a slightly different connotation; it implies that all the other children in the class are thirteen, which could happen, but is fairly improbable.
Like the other children in his class, John is thirteen years old.
english.stackexchange.com/users/2386/Jonathan Leffler
To me it sounds like a contraction of: Like many before, here is another
english.stackexchange.com/users/9625/719016
I've come across "like many another" in a GMAT question. Its use is similar to "Like many other" e.g. "Like many another in his class, John is thirteen years old."  It has 1M hits in google (compare to 135M for "like many other").I would like to know if it's a mistake or an uncommon but standard phrase.
Is the phrase "Like many another" correct in standard English?
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<grammaticality><phrases><determiners><many-a>
english.stackexchange.com/questions/4797
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There is no clear agreement as to whether "like many another" is correct English or not. However, it is referenced in the Meriam-Webster Dictionary to express "each of a large indefinite number". Regardless, it is likely to be very archaic and would not be used in formal contexts. The Free Dictionary and Merriam-Webster state that "many a/another" mean "each of a large indefinite number"Another" is a contraction of "an other" but given "a/an" imply a singular form, using "many other" seems incorrect.Never seen before, but not considered correct."Many a" is an idiom, and is a remnant of a construction that no longer exists in English, so "many another" as an extension also sounds incorrect.
There is no clear agreement as to whether "like many another" is correct English or not. However, it is referenced in the Meriam-Webster Dictionary to express "each of a large indefinite number". Regardless, it is likely to be very archaic and would not be used in formal contexts.  "Many a" is an idiom, a fossilised remnant of a construction which is no longer productive in English. The phrase 'like many another' is perfectly legitimate, though possibly slightly old fashioned.  
Like many another' may well be legitimate, though possibly slightly old fashioned and unknown to many. "Like many other" is much more widely used. There is no clear agreement as to whether "like many another" is correct English or not. However, it is referenced in the Meriam-Webster Dictionary. Regardless, it is likely to be very archaic and likely not suitable even in formal writing.
The Free Dictionary and Merriam-Webster state that "many a/another" mean "each of a large indefinite number" "Another" is a contraction of "an other" but given "a/an" imply a singular form, using "many other" seems incorrect. Never seen before, but not considered correct. "Many a" is an idiom, and is a remnant of a construction that no longer exists in English, so "many another" as an extension also sounds incorrect.
 "Many a" is an idiom, a fossilised remnant of a construction which is no longer productive in English. The phrase 'like many another' is perfectly legitimate, though possibly slightly old fashioned.  
It appears that this expression is referenced in the Merriam-Webster dictionary. There is no clear agreement about whether this is a standard or correct phrase in English. This phrase could be very archaic and not suitable even in formal contexts.