It is well known that, as CGEL puts it (p. 391),
Determinative another derives historically from the compounding of the indefinite article and the adjective other; the consequence of this for the modern language is that the existence of the determinative another blocks the co-occurrence of the indefinite article and other as separate syntactic constituents: *an other book.
Thus, an another would, in effect, contain two indefinite articles in sequence ('an an other'). Therefore, it should be unacceptable. It is indeed condemned as such here, here, here, here, and here.
Nevertheless, published literature seems to contain a surprising number of usages of an another. In what follows, I will try to include only works that 1. are likely written by native speakers; 2. do not contain other obvious errors nearby that would signal substandard editing; 3. are from not too-distant past. One could dismiss these as simple mistakes, except... when a mistake becomes widespread enough, it ceases to be a mistake, and becomes an acceptable alternative usage. Here, then, are ten examples of an another from published literature:
[1] If not, place it in an another pile, to be reviewed again. (source)
[2] Because the meaning of the words that are used to express thoughts are unique to each individual, there is an another unbridgeable gap between one person's thoughts and those of another. (source)
[3] In an another embodiment, the kit further includes a peripheral vascular access structure for peripheral implantation in a patient. (source)
[4] The deliberate indifference standard is met when a person knows of, and yet disregards or ignores, an excessive risk to an another's health or safety. (source)
[5] Skinner saw no reason to relate his data to data arrived at an another level of observation by other sciences. (source)
[6] Croce diagnoses Hegel's confusion about distincts as what anglophone philosophers since Ryle have called a 'category mistake.' To think of a piece of art as evil, an intellectual achievement as useful, or a properly functioning object as beautiful is like thinking of the university as an additional building on campus, team-spirit as an another player on the team, or the Average Tax Payer as a fellow-citizen. (source)
[7] In an another study, 24 patients status post hysterectomy received postoperative IMRT... (source)
[8] In September 1795, she returned to England, but finding Imlay living with an another woman, she again attempted suicide, this time jumping into the Thames River. (source)
[9] Pertaining to an organism that lives as a parasite on an another animal. (source)
[10] More suspicious was the discovery by the U.S. Office of Strategic Services (OSS) that De Amuedo had purchased, in cash, a $7,500 draft and an another $500 in traveler's checks at the San Juan branch of the Bank of Nova Scotia. (source)
As best as I can tell, in all of these examples, one can (and probably should?) drop the an in front of another. Even allowing for the possibility that sometimes an another could be acceptable, in these examples, I can't detect any believable change in meaning if the an is dropped.
The above is hardly an exhaustive list; I am sure there are many more examples. I have only gone through a fraction of hits from this search on gooogle books (note that most of these hits are false positives, though, usually consisting of an' another, which in reality is and another).
Question:
Can we really dismiss examples like these as mere mistakes? I am tempted to say 'yes', and yet... there seem to be too many of them. Could it be that an another is at least marginally acceptable now?
