Can you have two primary buttons?
Don't have more than one primary action button on the screen at a time. Let users focus on the task at hand. You can have more actions on the page, but make sure there is only one primary. Users have expectations of what a single button on a page will do, based on the page they are on.
What is a split button?
A split button is a hybrid between a button and a menu: it groups related commands together into a dropdown, but also offers one-click access to a default choice that doesn't require opening the menu.