Can another type of session be built from scratch?

I used to have Cairo Dock along Unity and I could switch to an Environment made with Cairo dock form the login screen. Wehn I install Cairo in Ubuntu MATE I don’t get two session types like I did in Unity DE. Just as if I installed Plasma Desktop I would get that session option from the login screen.

Is there a way to achieve this with Cairo and MATE?

To set another option in the session menu and have it below MATE session.

Here is a reference of what I mean: https://www.youtube.com/watch?v=Qpe7lCQmwNA