If I’m a dual citizen, can I have an International Experience Canada work permit under each citizenship?

Yes. For example, you can get a work permit once as a citizen of the United Kingdom and a second time as an Irish citizen

To do this, you need to:

• have a valid passport issued by the country you're applying under,
• meet all of the eligibility criteria for this country, and
• provide a letter of explanation in your work permit application that says
  • you are a dual citizen
  • your other work permit is under your other country of citizenship.