For a rail-to-rail output stage: I suggest looking at the Monticelli output stage, which was published back in the late 80's:
Author: D.M. Monticelli.
Title: "A quad CMOS single-supply op amp with rail-to-rail output swing".
Publication: IEEE Journal of Solid-State Circuits, Volume: 21, Issue: 6, Dec 1986.

This output stage was examined in detail by Horowitz & Hill in their book "The Art of Electronics: The X Chapters", which you may be able to find at this link:-

https://x.artofelectronics.net/wp-content/uploads/2019/11/4xp11_RR_op-amps.pdf

PS: seems that link in your post is broken.

For a rail-to-rail output stage: I suggest looking at the Monticelli output stage, which was published back in the late 80's:
Author: D.M. Monticelli.
Title: "A quad CMOS single-supply op amp with rail-to-rail output swing".
Publication: IEEE Journal of Solid-State Circuits, Volume: 21, Issue: 6, Dec 1986.

This output stage was examined in detail by Horowitz & Hill in their book "The Art of Electronics: The X Chapters", which you may be able to find at this link:-

https://x.artofelectronics.net/wp-content/uploads/2019/11/4xp11_RR_op-amps.pdf