Hello kwizzo,
The behavior you are describing is not something that can be done on a single button or event but there are a few work arounds to your desired outcome.
1. Create 1 form with 2 views and 2 data connections.
For this scenario, in the first view you would have the use fill out the necessary information, and on submit you would submit data via the first data connection, and then switch views to the other "form" and on submit send data on your second data connection.
2. A button and a link in your form
For this scenario, you would have a 2 step action for your user. The user would need to submit the original form, and then click a link to open your separate form.
Hope that helps!
Bre