The trick is not to use the master branch to create pull requests. Then you won't need to create multiple forks since you can make as many branches as you need and make pull requests against each branch independently.
Given a clean forked repo, create a dedicated branch and use that branch for the pull request.
You can create branches from the web UI (although it is not obvious).
Click the branch selection dropdown, type the new branch name in the input field, and then you'll see a clickable link Create branch: <new-branch-name> as shown below. The tricky UI part is that it might not be very obvious you should click the "create branch: xyz..." — it is NOT displayed as a button or as a hyperlink, and there is NO indication that this is a clickable link. Moreover, there is NO hint whatsoever that a branch can be created until you type in the search box — anyone would probably assume that the search box is used exclusively for searching branches, and not for creating them.
![github web create branch]()
In case you already made changes directly in your fork's master branch then consider moving those changes into a dedicated branch and hard resetting the master branch to the original remote so that you keep it clean for synching with the upstream repo.
See also: