Yes you can have multiple remotes registered for your repository.
You have to add the new remote to your new repository. Generally main repository is named origin
and the original repository (from what your forked or in your case the backup repository) is named upstream
.
So what you can do:
git remote rename origin upstream # change your current 'origin' remote to 'upstream'
git remote add origin git://foo@bar.spam # add your new remote
Then, you will be able to fetch and push on both.
If your upstream is used as backup, I suggest to only push master
(and eventually develop
if you are using gitflow or something similar) to upstream
.
So your upstream
only stores your merged code when your origin
stores every branches & commits.
But it depends what you need.
Here is a stackoverflow thread about origin & upstream remotes: What is the difference between origin and upstream on GitHub?