How can I wrap a multi-line quote in GFM?

If you're using kramdown, you can use break   or multiple   break tag. As you know, the break tag inserts a single line break.

Lorem ipsum dolor sit amet

Result:

Lorem
ipsum

dolor sit amet

There is no way to do that in pure Markdown, nor in GFM.

If you use line breaks instead of paragraphs, you only need one >:

> Lorem[space][space]
ipsum[space][space]
dolor sit amet

Result:

Lorem
ipsum
dolor sit amet

Related