word choice - "Another" vs "other"

I don't know when can I use another and when I should only use other. At first, I thought another should be used only when a singular word comes after it. This is what Theodore Bernstein says in The Careful Writer: A Modern Guide to English Usage (1965):

ANOTHER The word is often misused for more, others, or additional. A typical newspaper example: "The port directly employed 250,000, with another 150,000 indirectly employed." Another means one more of the same kind. In the sentence quoted it would be correct only if the second figure were the same as the first.

But then I saw in the OALD8 an example with another attached to a plural noun similar to the one Bernstein gives as an example of "misused" another. Is it wrong to use another to say things like "another three things"? Is it better to say "three other things"?

Answer

Can “another” be used with plural nouns provided periods or measurements don’t count?

An add-up:

• Another (another + singular nonspecific countable noun)


• Other (other + plural or uncountable nonspecific noun)

You can say: 'If I had another five dollars I could afford it.' - Five dollars is single unit of money.

I have to admit that this answer lacked more information previously.
With numbers it is acceptable to use another, but there are
exceptions. I have done a research in Hornby and Swan books and I have
found out an interesting piece of grammar.

Examples:

• A have another three questions - Here "three questions" is a set of questions, a "singular nonspecific countable noun" so it is right to say so.




• Another three tanks will come later - Another good example where "three tanks" is one set.




• I have another four miles to run - Four miles is a distance.

But we can't use another with possessive determiners:

• My another three books - is incorrect. Instead we should say "My three other books"





• His another two brothers - is also incorrect. "His two other brothers" is correct.