In your github fork, you need to keep your master branch clean, by clean I mean without any changes, like that you can create at any time a branch from your master. Each time that you want to commit a bug or a feature, you need to create a branch for it, which will be a copy of your master branch.
When you do a pull request on a branch, you can continue to work on another branch and make another pull request on this other branch.
Before creating a new branch, pull the changes from upstream. Your master needs to be up to date.
Create the branch on your local machine and switch in this branch :
$ git checkout -b [name_of_your_new_branch]