No, you really don't want to do this, it makes a total mess of your project. It inevitably leads to "I thought someone else was doing it".
Keep the assignee as the single point of responsibility for an issue, even if it changes a lot. If you need to associate other people, then use a custom field to represent "other people who might take it on if <assignee> is failing to be responsible" - either a group custom field, or a multi-user picker. Or if you have Service Desk, use Queues.
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