For RPLIB libraries that are hosted at Axure Share, a workspace member can download an editable copy when they log in at share.axure.com, open the workspace, hover over the gear icon along the right-hand side of the project, and select "File + Settings". You'll be able to download a copy by clicking the file name on the resulting page. (Team projects on Axure Share do not have an accompanying project file that you can download and edit.) This is certainly one option for multiple users to download, edit, and re-publish to the same library.
Generally speaking, the option "Edit Library" in the Libraries pane is only enabled if the loaded widget library is stored locally on the computer. If a user would like to edit a library, they'll need to obtain a copy of it. To do that, they can store either a regular RPLIB or a team project library RPLIBPRJ. Once you load either an RPLIB or RPLIBPRJ into Axure RP, the "Edit Library" option will be enabled for it in the Libraries pane.
It sounds like you're looking to take the route of a team project library (RPLIBPRJ), and you've created it already. Now that it's created, each new co-author will need to retrieve a local copy of the team project via the RP menu "Team > Get and Open Team Project" and select the preferred storage location at that stage. This local copy will have the extension ".rplibprj", which is the team project library that you can load into an instance of Axure RP in the Libraries pane. Once you make changes to this stored local copy, you can check in the changes via "Team > Check in [Page]". To retrieve changes from the team directory, select "Team > Get All Changes". Once you load the RPLIBPRJ into Axure RP, the "Edit Library" option will be enabled. And you can select "Refresh Library" in the Libraries pane to show the latest changes that were retrieved in the team project lib.
The workflow can vary depending on the team, whether everyone needs to be co-authors, etc. We currently do not have a step-by-step tutorial that covers every use case. I'll be happy to get the ball rolling on that, though. To that end, please let me know the details surrounding your specific team setup, whether all users need to be co-authors of a team project library (RPLIBPRJ), etc.
Hopefully that helps!