I would like to change the email notifications to only be generated if a change is made by a JIRA user that is not the assignee, is this possible?
No, it's not. The notification schemes send to everyone nominated in them. All you can really do here is make the scheme as quiet as possible. Avoid the use of groups and keep the roles down to a minumum
You might also want to check people's account settings - the "do NOT email me on my own changes" flag is very useful
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