I thought of a way to implement multiple references to the same footnote without breaking HTML links between footnotes.

You could allow for the creation of multiple footnote links from the text into footnotes that point to the same footnote, with a sequence of different secondary designations. For example, footnote 1a, 1b, 1c... all could point to Footnote 1. Then, in the footnote, you could open with 1 a b c ..., with the different letters providing alternate linkbacks to the other places in the text.

This is how Wikipedia handles multiple referencing to the same citation, so there's precedent. And using some light formatting or option selection, it could support a lot of the ways that people want to use footnotes more complexly, from "I don't want fifteen footnotes that just say 'ibid'" to "Working on a House of Leaves inspired labyrinth of text."