What's the problem with you?
You can add another web part by clicking "Add a Web Part" button as your screenshot.
If your page is in Site Pages library, you can go to SharePoint Designer->Site pages in the left pane->find the page and Edit File in advanced mode.
Add insert Web Part Zone via click the botton:
In Order to add a new WebPart Zone you need to create a custom Page Layout and use that page layout to create your SharePoint Pages OR you can edit your page in SharePoint Designer and add below code snippet to it.
Reference: Create a Custom Page Layout in SharePoint.
Then you can add below code snippet to add webpart zone to your custom page layout: