With a little black magic, yes.

Step 1

We need to understand that

git diff

lists files, change sets, removals, additions and some lines around them

Step 2

We need to remove all superfluous lines, so that we get only the files and the changes inside them, like this:

git diff | grep '^\(+++\|---\|-\|+\)'

Step 3

Write a program that runs the command seen at Step 2 and displays the result. I know this is not yet the solution, but you will absolutely need this step to be performed first, so we know that the input and the output are working.

Step 4

Now, let's apply filtering. A very simple filter would be performed by this algorithm

deletedLines <- empty
for each line
    if (line starts with --- or +++) then add line to output
    else if (line starts with -) deletedLines.add(line)
    else
        if (line starts with + but not with +++) then clear deletedLines
        else add deletedLines to output
end for

git diff | awk '/^@/{ if(s) print p; s = 1; p="" } 
    s == 1 && /^\+/ { s = 0 } 1 {p = sprintf("%s\n%s", p, $0)} 
    END { if (s) print p }' s=2

An alternative solution, in a single line, and using just regular expressions. Here, I use rg, but any grep tool that supports multiline matching and inverse matching (-U and -v, respectively) will work.

git diff | rg '^(\+ |- ).*' | rg -vU '^-(.*)\n\+(.*)\n'