I think changing Jitter settings is only option you have if you want to use Points. Could it be possible to use other visualization such as bar chart?
![jthi_0-1673515338987.png jthi_0-1673515338987.png](https://community.jmp.com/t5/image/serverpage/image-id/49007i7DDE3DD49DB3D6B8/image-size/medium?v=v2&px=400)
Instead of
![jthi_1-1673515346777.png jthi_1-1673515346777.png](https://community.jmp.com/t5/image/serverpage/image-id/49008iE9745C1945F9DBFC/image-size/medium?v=v2&px=400)
You can use Customize menu to change Marker's Jitter settingsin more detail (especially Axis and Jitter type)
![jthi_2-1673515640595.png jthi_2-1673515640595.png](https://community.jmp.com/t5/image/serverpage/image-id/49009iCA7113E0F9D82326/image-size/medium?v=v2&px=400)
![jthi_3-1673515715976.png jthi_3-1673515715976.png](https://community.jmp.com/t5/image/serverpage/image-id/49010iD865871EF3366F63/image-size/medium?v=v2&px=400)
Also going through Essential Graphing from JMP Help page can give some other ideas
-Jarmo