tmp_npm.sh

#!/bin/bash

BASE_DIR=${TMPDIR:-/var/tmp}
ORIG_DIR=$PWD
HASH_CMD="md5sum"

DIR_NAME=`echo $PWD | $HASH_CMD | cut -f1 -d " "`

TMP_DIR=$BASE_DIR/$DIR_NAME
mkdir -p $TMP_DIR

pushd $TMP_DIR

ln -sf $ORIG_DIR/package.json
npm $1

# Can't use archive mode cause of the permissions
rsync --recursive --links --times node_modules $ORIG_DIR

popd

Amazing script.
Vagrant 1.9.1, NPM 3.10.10
I put this in my folder.
And run such as "sudo npm install --save-dev mocha".
Then it works.