You can configure multiple remote repos using git remote command:
git remote add alt alt-machine:/path/to/repo
To fetch from configured remotes (but not merge into HEAD) do:
git remote update
If you are not connected to one of the remotes it will throw you an error which you need to fix it manually with a merge or cherry-pick depending on how you want to make changes.
To fetch the master branch from alt and pull it into your current head, do:
git pull alt master
In fact, git pull is almost shorthand for git pull origin HEAD.
Thus you can pull or push from multiple locations.