Will it simply associate modifiers right-to-left? As in, the rightmost modifier modifies everything to the left of it, etc. What I'm getting at is that I don't want to have to think about something like "modifier precedence" when chaining them like this.

It'll be strict right-to-left. Just don't throw mys in there, as proper scoping in chained modifiers is never what people expect, and may well just be disallowed.