I did agree with you two until I reread Quirk et al.'s "A Comprehensive Grammar of the English Language" today and learned that personal pronouns like "his", "my" etc. belong in the central determiner category, while general ordinals like "another" belong in the postdeterminer category. According to his research, central determiners can cooccur with and usually precede postdeterminers. That is, theoretically "his another son" is a permissible concatenation.
As you two also regarded such cooccurrences as of erroneous use, I then googled "his another *". Much to my surprise, I find many hits. I then followed it up with some reputable newspapers in case google findings are not reliable. Again I find the following sentences (I might have done even better if I could get access to large corpora like the BNC.):
- He was working on his another book, Too Much Money, at the time of his death from cancer. ("The Times", 28 August 2009)
- Pennock injured his another pitcher's battle from Cleveland pitching hand when he stopped a line drive by Sewell and had to retire. ("The New York Times", 16 July 1921)
So, how would you explain the above two? Personal idiosyncrasy?