Currently, the answer to this question is that, "You don't."
You can still post events to other sites in our network. To do so, you would simply start your submission from the particular calendar page you would like to post to. When you post to that calendar, your event will appear on that calendar even though your login to may direct you to a dashboard that is showing the logo for a different site.
Users in our system can only belong to one publication at a time. The publication that your account belongs to is determined by the site you used when you first submitted an event to our calendar system.
In the case that your event does not get posted to that calendar, it is likely that the location or category of your event did not match the settings for that site. If you are ever unsure of where you event was posted, please refer to this article: Where is my event?