My first (and simplest) idea to do this would be use of "Local Data Filter" in "Fit Y by X",
there you have high flexibility to switch between different subsets.
If there is no other reason to really create a subset-table, I would prefer this in JMP.
See example for Big Class subset Female.
With the additional subset there is another issue, you need to handle and store 2 tables then, and the fit x by y script is based on and saved in the subset table.
With Local Data Filter (or suggestion of @statman to use "by") you can store the script in the original table, and need to store only one table.
Georg