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When can you use an underlined superscript "o"? I know that it is used for numero

Can it be used for company?

C°

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This is what's known as the "numero sign" or "numero symbol". It actually has its own unicode character: №. As such, it's considered a single character, not two.

From Wikipedia:

The numero sign or numero symbol, №, is a typographic abbreviation of the word number(s) indicating ordinal numeration, especially in names and titles. For example, with the numero sign, the written long-form of the address "Number 22 Acacia Avenue" is shortened to "№ 22 Acacia Avenue", yet both forms are spoken long.

Typographically, the numero sign combines the upper-case Latin letter N with a usually superscript lower-case letter o, sometimes underlined, resembling the masculine ordinal indicator.

The Oxford English Dictionary derives the numero sign from Latin numero, the ablative form of numerus ("number", with the ablative denotations of: "to the number, by the number, with the number"). In Romance languages, the numero sign is understood as an abbreviation of the word for "number", e.g. Italian numero, French numéro, and Spanish, Portuguese and Galician número.

As far as I know, there is no official name for "C°", but I believe the "o" would qualify as a superior letter.

There is certainly precedence for using the same typography style for "Co", so it gets a thumbs up in my book. Here's an example:

Bedat & Co logo Source: Wikipedia

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I'll add that there is precedence for a huge number of abbreviations. I work regularly with 19th century items and the no/co thing is a typographical convention which rose from the idea of avoiding hand cramping when writing (read: laziness). People often forget that in days before carbon paper, people were employed to hand-write duplicates of all written correspondence. –  horatio Dec 5 '13 at 19:26
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