Yes. You can copy an existing campaign by selecting the campaign on Campaign List then selecting Actions>Copy Campaign.
A new window will open to allow you to rename the campaign from its default of "Copy of Campaign Name." All of the information from the original campaign, including the campaign info, recipient list, and template will be carried over to the new campaign. Once you click create, you can then use View/Edit to make any changes to the campaign you would like including updating or changing the recipients list and editing the template.