Learn English – How to punctuate around parentheses

"Does English allow..." is a problematic question, as English has no authoritative body to allow or disallow anything. As an attempt to provide a standard, several bodies issue "style guides", among the most influential of which are The Chicago Manual of Style, The MLA Style Manual, The MLA Handbook, and The AP Stylebook. They each have different histories and target audiences, so different editors and publications choose different ones for their own reasons. So to answer your question with authority you would need to consult the relevant style guide. For most purposes (writing that is neither academic nor journalistic) I use the Chicago Manual of Style.

As a general rule, though, (and according to the Chicago Manual of Style as I understand it) parentheticals should not be as long as a paragraph, and would typically be converted into a footnote instead. In some kinds of publications, they would be margin notes or endnotes.

If you just wanted to be ornery, you would probably follow the rules for including multiple paragraphs inside double-quotes and repeat the left parenthesis at the beginning of each paragraph, like this:

(Paragraph 1.

(Paragraph 2.

(Final paragraph.)

See The Chicago Manual of Style, 16th edition, Section 13.30, for how to quote multiple paragraphs.

The double parentheses indicate an interpolation which would normally be indicated with brackets:

But he told me the U.S. military said he couldn’t come because of the [State Department] travel advisory here.

The brackets enclose text which is not actually part of the quotation but necessary to provide additional context, to allow full understanding.

Using single parentheses would not provide the level of “offset” which the interpolation needs: if the speaker himself had used a parenthetical clause it would be indicated with single parentheses. Double parentheses indicate that it is not the speaker’s interpolation but the reporter’s.