Solution 1:

Let's say that you have a block quote like this:

Apple pize are my flavorite, not because their combination of fruit and cinnamon, of tart and sweet and spicy delivers a perfect medley of olfactory and gustatory delight, but because—as Travis Bickle makes clear in Taxi Driver [1976, directed by Martin Scorsese]—they invite (and indeed insist upon) a temporary resolution of the perennial philosophical choice between cheese and no cheese.

and you're bothered by the spelling mistakes at words two and five. You could (as rand al'thor points out) retain the square brackets that appear in the original quotation after Taxi Driver, and put your sic additions in curly brackets to distinguish them from the built-in square brackets. But doing so doesn't establish beyond the shadow of a doubt that the curly brackets are yours and the square brackets are the original author's. To accomplish that, you'd have to point out in a note somewhere that the curly brackets are yours and the square brackets are the original author's.

And if you adopt the curly bracket treatment this time, what happens when you have another block quote later on that doesn't have built-in square brackets from the author but that (like the first block quote) does have typos that you want to distance yourself from? Do you again put sic in curly brackets, even though the original block quote has no square brackets; or do you switch to square brackets and add another note, this time letting readers know that the square brackets are yours?

I think a more elegant solution is to warn the reader about who is responsible for what prior to the first block quote, and not to use sic at all. For example, you might say this:

Mrs. Crocker hints at her not-yet-fully-developed views on pie and eschatology in an early musing on traditional American desserts and film (all spellings and the instance of brackets are in the original):

Apple pize are my flavorite, not because their combination of fruit and cinnamon, of tart and sweet and spicy delivers a perfect medley of olfactory and gustatory delight, but because—as Travis Bickle makes clear in Taxi Driver [1976, directed by Martin Scorsese]—they invite (and indeed insist upon) a temporary resolution of the perennial philosophical choice between cheese and no cheese.