Plus or Minus

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start, letter

The six-letter entries can be filled into the grid as is.

start, square

The legend to the right of the grid says that of the 36 squares in the grid, 3 are of one type and 5 of another. The squares indicate what happens to across and down answers passing through them.

letter, short

The four-letter entries can also be finagled into the corresponding rows and columns, but with two extraneous letters. Some of these correspond to the 8 squares that have minuses.

square, minus

When an entry hits a plus as it enters a square, the letter in that square is appended to the entry as normal. When an entry hits a minus, the letter in that square is instead removed from earlier in the entry. This cancels out an earlier plus, accounting for the four-letter entries.

extract, minus

To extract, examine the 8 special squares.

1 2 3 4 5 6

[See original puzzle for image]

1. Suffers from illness (4)1. Word with special or display (4)
7. Pope John Paul II or Marie Curie, e.g. (4)2. Advanced H.S. lab class (2 4)
8. Download without permission, in a way (6)3. It was first transplanted in 1905 (6)
9. Alternative to the other thing? (4)4. Like 1080p video (2 2)
10. High schooler or eighth grader, perhaps, but usually not a sixth grader (4)5. It’s part of a building in English but it’s part of a sandwich in Italian (4)
11. Like a mafia man (4)6. Bristle (6)