While you can do this by writing a small shell utility script i.e. to pull from two remotes. But if you are collaborating on a project then I will recommend using a time-tested workflow for git. Bitbucket has listed a couple of them in the tutorials, but the most impressive workflow as per me is Gitflow. Do check it out here https://www.atlassian.com/git/tutorials/comparing-workflows/gitflow-workflow.
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