Can a greedy algorithm have more than one subproblems to solve after making greedy choice?

Question

For example: s = <s1 s2 s3> is my problem,

I make greedy choice s2 and solve s1 and s3 in a greedy way.

In CLRS, it was mentioned regarding "designing greedy algorithms"

Cast the optimization problem as one in which we make a choice and are left with one subproblem to solve

So why is it that we are left with only one subproblem in greedy method after making greedy choice?