I think there's a slight confusion here, possibly caused by the use of language on-screen and in Atlassian's docs (not by us end-users!)
There are two things being discussed as though they are the same thing, and they are not.
Project Type
As shown in the screenshot in the original question, these project types are a way of grouping projects together. They are supplied by the three applications - JIRA Core gives us "business", JIRA Software gives us "Software" and JIRA Service Desk would add "Service Desk" to the list.
Applications add these groups. I think they can also be added by add-ons, not just the applications.
Project templates
These are different configurations used when creating a project, which try to help you get the config for a different style of project right. There are several templates for each project type. The templates also set the project type on the project when they are used to create a new project. They are all handled by (built in) add-ons, and you can write your own templates, and use the rather excellent Wittified add-on that Bart refers to for managing and creating them too.
So, either way, you're going to need to do something in an add-on to create a fourth type and it's not as simple as just creating a new project template.
So am I right in assuming that Wittified add-on doesn't allow you to create new project types? As mentioned in the original question?
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The last time I used it, no, it could not create new project types, it was for handling templates. As far as I can tell it still doesn't.
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You need to create a template, check this documentation: https://developer.atlassian.com/jiradev/jira-platform/guides/projects/tutorial-creating-a-project-template
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HI
For custom project types you need to develop your own template or else you can find already developed Add-on here.
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as me and @Bart Meerveld mentioned in above comment you need to develop your own Template or else you can Add-ons.
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Where exactly does the plugin allow you to create new project types?
I haven't explored it extensively but from overview, all I could see is that it helps you just create projects?
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https://wittified.atlassian.net/wiki/pages/viewpage.action?pageId=55378126
It's in the plugin documentation.
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