Sharepoint - Customize newform save button - Save and redirect to another form

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)

https://xxx.sharepoint.com/sites/VM/Lists/Tasks/NewForm.aspx
?Source=
 https%3A%2F%2Fxxx.sharepoint.com%2Fsites%2FVM%2FLists%2FTasks%2FAllItems%2Easpx
&RootFolder=

So if you replace that Source with URL of a NewForm

https%3A%2F%2Fxxx.sharepoint.com%2Fsites%2FVM%2FLists%2FTasks%2FNewForm.aspx

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

You can do it with JavaScript code or put a hidden ListView WebPart on the NewForm page that lists the last created item and then use some script to extract what you need and update the fields in the Form

... takes just a bit of scripting