Confused about site maps for add-on domains

[anglotexian]

Hello, I have an existing site for which I have successfully created a site map and have been indexed by Google. Now I have purchased two add-on domains with product-specific names which point to pages at the original site. Internal navigation permits all three domains to access the whole site. Is it possible to generate site maps for the add-ons , and if so would Google penalize me for having multiple entry points to the same site? Should I create unique gateway pages for the add-ons to prevent issues?