Can a greedy algorithm have several sub-problems to solve after making a greedy choice?

For example:
s = is my problem,

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

In CLRS, it was mentioned about "the design of greedy algorithms"

Define the optimization problem as a problem in which we make a choice and are
left with a sub-problem to solve

So, why does there remain only one sub-problem in the greedy method after making a greedy choice?