Help with a quick grammar question?

I know that for Chicago MLA format I should always put a comma, period, semicolon, or colon (rule sometimes excluding question mark and exclamation point) inside the endquote of something I’m citing from someone else’s text – but what if I’m quoting, and the writer puts a quote of her own in, or emphasis-quotes around a particular word, like so: “Uncanniness…puts Dasein’s Being-in-the-world face-to-face with the ‘nothing’ of the world; in the face of this ‘nothing’, Dasein is anxious with anxiety about its ownmost potentiality-for-Being.” The part I’m wondering about is the ”...this ‘nothing’, Dasein…” – do I switch this alternative comma-quotation mark style into my own, or stay true to the quote?

Edit – I can’t find anything about this in the manual or online.