One admin or member can be part of only one account at a time. So if you have a team member on a different account that you need to add to a new account, you need to remove them from the other account and add them to the new one.
You can use multiple email accounts or aliases for the same user to create additional accounts if you need to.
If you use Google for business for your email, you can also create any number of aliases on the fly as below:
If your email id is firstname.lastname@example.org, any email id of the format name+<something>@mydomain.com is automatically treated as an alias. For example, you may use email@example.com, firstname.lastname@example.org as aliases with which you can create separate accounts on Freshchat.