You can get the same effect by adding an extra push URL for your origin remote. For example, if the URLs of your existing remotes are as follows:
$ git remote -v
origin me@original:something.git (fetch)
origin me@original:something.git (push)
my_other_remote git://somewhere/something.git (fetch)
my_other_remote git://somewhere/something.git (push)
You could do:
git remote set-url --add --push origin git://somewhere/something.git
Then, git push origin will push to both repositories. You might want to set up a new remote called both for this, however, to avoid confusion. For example:
git remote add both me@original:something.git
git remote set-url --add --push both me@original:something.git
git remote set-url --add --push both git://somewhere/something.git
… then:
git push both
… will try to push to both repositories.