Edit, 30 May 2020: In Git 2.15 or later I recommend using git worktree instead of trying to do the below. There are some restrictions on added work-trees that make them somewhat annoying for this kind of work-flow, but it can work, and is built in to modern Git.
Note that if you do do something like I describe below, git gc won't know to look in your alternate index files, and in fact, from its original introduction in Git 2.5 until it was fixed in Git 2.15, git gc forgot to check added work-trees and their index files!
See VonC's answer for more.
You can in fact have multiple different staging areas (more literally, multiple index files) in git. To achieve the effect you want you would have to write your own variant of git add -p anyway, so what I will do here is sketch an outline, as it were, of how to do this.
The default index file—the one git uses if you don't direct it to some other index file—lives in .git/index (or, more shell-correctly, $GIT_DIR/.index where $GIT_DIR is taken from the environment or, if not set there, from git rev-parse --git-dir).
If you set the environment variable GIT_INDEX_FILE, however, git will use that file instead as the index. Thus, you might begin your "scatter changes to four branches" process by doing something like this:
GIT_DIR=${GIT_DIR:-$(git rev-parse --git-dir)} || exit 1
index_tmp_dir=$(mktemp -d) || exit 1
trap "rm -rf $index_tmp_dir" 0 1 2 3 15 # clean up on exit
# make four copies of initial staging area
for f in i1 i2 i3 i4; do
cp $GIT_DIR/index $index_tmp_dir/$f
done
# THIS IS THE HARD PART:
# Now, using `git diff-files -p` or similar, get patches
# (diff hunks).
# Whenever you're ready to stage one, pick an index for it,
# then use:
GIT_INDEX_FILE=$index_tmp_dir/$which git apply --cached < diffhunk
# Once done, commit each index file separately with some
# variation on:
for f in i1 i2 i3 i4; do
GIT_INDEX_FILE=$index_tmp_dir/$which git commit
done
For the part labeled "hard part", your best bet might well be to copy git's add-interactive perl script, found in $(git --exec-path)/git-add--interactive, then modify it to suit. To remove the "exactly four commits" restriction, make this modified interactive-add create a new index file dynamically (by copying the original, or perhaps creating an "empty" index equal to the HEAD commit or whatever; see git read-tree as well).
Edit: the some variation on section really should almost certainly use git write-tree and git commit-tree to make new branches out of each of these commits, using the parent of the current commit as their parent, rather than allowing git commit to string the commits together as a linear chain. That means one must also choose some naming scheme for these various newly-created branches.
