One of our team members has most of her tickets in other projects, as she works with multiple teams. Would we be able to have some of her tickets be shared between our project and another project. We would prefer to avoid duplicating tickets if possible.
Issues, by definition, belong in a single project. If you have pieces of work that span different projects, you should look at your project structure (it's not matching how you work), or split the issue into pieces, one for each project that needs to look at it.
It's not quite a case of duplicating it, it's a case of splitting it into the actual tasks that need to be done, and I'd recommend llinking them together, or include them in an Epic if you have Jira Software.
I like what Nic and Joe are saying about linking issues between projects. If you would like for both the original issue and linked issue to close out when the other is closed, consider a scripting solution as found in the Atlassian Marketplace. Here is an example on how to do this using Automation for Jira:
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