You can use multiple remote repositories with git. But you’ll have to push separately into 2 of your remotes I believe.
For example, if your project currently points to github, you can rename your current remote repository to github:
$ git remote rename origin github
You can then add another remote repository, say bitbucket:
$ git remote add bitbucket git@bitbucket.org:your_user/your_repo.git
Now in order to push changes to corresponding branch on github or bitbucket you can do this:
$ git push github HEAD
$ git push bitbucket HEAD
Same rule applies to pulling: you need to specify which remote you want to pull from:
$ git pull github your_branch
$ git pull bitbucket your_branch