Add the URL of the next form as the &Source=[url] parameter
The Source parameter in the URL is where the browser is redirected to after a Form is saved.
Open an EditForm and investigate the URL
The URL has to be URL encoded (and it needs to be within the SharePoint domain)
So if you replace that Source with URL of a NewForm
You can add an item and then be returned to a Blank NewForm
On that new form you will have to add code to retrieve the last added ID
... takes just a bit of scripting