"... 1) ..bla-bla.. 2) ....bla-bla.. 3) ....bla-bla...
Однако для новой теории у нас нет ни того, ни другого, ни третьего"

Он мне предложил перевод типа
"We possess none of the three items ..."

что мне совсем не нравится. Что тогда, остается вариант типа
"none of either items"...?

Мне тоже английский язык не во всём нравится. Но другого нет.

"Не знаете вы ни меня, ни себя, да и вообще ничего."

"You know neither me, yourselves nor any thing".

правда примеров на " more things " не дают))

http://dictionary.cambridge.org/ru/словарь/английский/neither

«neither: not either of two things or people:
We've got two TVs, but neither works properly.
Neither of my parents likes my boyfriend.
Neither one of us is interested in gardening.
"Which one would you choose?" "Neither. They're both terrible."
If she doesn't agree to the plan, neither will Tom (= he will also not).
Chris wasn't at the meeting and neither was her assistant.
informal "I don't feel like going out this evening." "Me neither."
On two occasions she was accused of stealing money from the company, but in neither case was there any evidence to support the claims.»

Neither French and German, nor English make any impression on them

Первые два отделяются в одну группу

Neither is used to mean none of two or more. Although some suggest that using the word neither with more than two items is incorrect, it has been commonly used to refer to more than two subjects since the 17th century.

И далее идут литературные примеры, включая Киплига (вот прямо из East is East, and West is West, and never the twain shall meet), из текста Jesus Christ Superstar и др. Или вот например, музыка в камне:

Но использовать в тексте неносителям я бы отсоветовал. Просто чтобы не вызывать инстинктивные беседы на эту тему.

Neither snow nor rain nor heat nor gloom of night stays these couriers from the swift completion of their appointed rounds

(unofficial) creed of the United States Postal Service

'neither' can be used with three or more items in some constructions, but is rare in other constructions.

* 'either a, b, c or d' – is correct.
* 'neither a, b, c nor d' – is correct.

In theory, according to some textbooks,

* 'either of the (three/four/etc)' – is OK and
* 'neither of the (three/four/etc)' – is also OK

but in practice most people say:

* 'either any of the (three/four/etc)' and
* 'neither none of the (three/four/etc)'

because most people associate 'either' and 'neither' with just two items. So if you want it to sound English, use 'neither of the two' but 'none of the (three/four/etc)'.

solidrain

** Вообще-то на "neither of the three" в Гугле хитов хоть отбавляй ... **
You've omitted to mention that:

* 'neither of the three' = 8,160 hits on Google
but
* 'none of the three' = 127,000,000 hits.

Draw your own conclusion ....

Что касается neither ... nor, в поддержку вашей точки зрения приведу цитату из моей «настольной Библии» - бумажного издания книги великого (не побоюсь этого слова) знатока английского языка Годфри Говарда (Godfrey Howard) “A Guide to English in the 21st Century”:

“It is not true, as some books still lay down, that ‘neither ... nor’ should be used about only two alternatives. You can say ‘Neither Mary, nor John, nor Harry, nor Susan turned up.’”