Is there a template for a cost share agreement addendum? How are these routinely handled in a project office?
Since Evolved NATO SeaSparrow (ESSM) is an Int'l Cooperative Program (ICP), the overall framework and guidance for ESSM's implementation is contained in the various ESSM Memoranda of Understandings (MOUs) signed by the partiicipating partner nations.
In general, questions like yours are addressed either in the ICP MOUs that established the ICP, the ICP MOU's Program Plan (or equivalent) approved by the MOU's Steering Committee (SC), or a specific SC Decision Memo (DM) that governs the process for establishing and modifying cost sharing implementing agreements among sets of partner nations such as the one you describe in your Question Background. You should review the ESSM MOUs, Program Plans, and DMs to see if any guidance or template exists for ESSM cost sharing implementing agreements since there is no 'general template' that exists (only program-specific templates established in each ICP program's MOU, Program Plan, and DMs).
The Navy's international programs organization, Navy International Programs Office (NIPO), has an International Agreements Division that has copies of all of the ESSM MOUs. They are also in the best position to provide advice and guidance on your specific question on which template to use to amend (modify) the existing ESSM cost sharing implementing arrangement to add a nation as an add'l partner in the specific effort being cost shared. We recommend you contact them directily and ask them for assistance. If you have difficulty contacting Navy IPO's Int'l Agreements Division, please send an e-mail to firstname.lastname@example.org and we can provide you with an e-mail address to use to contact them.