C++ :: Generalized Sort Function Using Lambda Functions

How to improve my customSort function. It is to accept a lambda function as parameter which customizes your sort in any special way you want.

#include <iostream>
#include <algorithm>
#include <vector>
#include <deque>
#include <functional>

enum personType {teacher, student, baby};

[Code] ....

For example, std::vector<Person> people = {Mark, MrMac, Lola, MsWhite, Cindy, Zainab, Mikey, Fred, Zolal} is to be sorted so that teachers will be placed first, then students, and then babies, but with the exception that people with names starting with Z be placed before anyone else, followed by people with age equal to 8. All this is set up by the ordered list:

person.name.at(0) == 'Z',
person.age == 8,
person.type == teacher,
person.type == student,
person.type == baby

So the output gives

Zolal
Zainab (baby)
Cindy
Ms. White
Mr. Mac
Fred
Mark
Mikey (baby)
Lola (baby)

Teachers are supposed to be placed before students, which in turn placed before babies, but Cindy's age is 8, and so is placed before the teachers, and Zolal and Zainab start with Z, so is placed before her. So far so good, but now I want the further sorting result that all people within their subcategories be sorted in their own way, e.g. Zainab should come before Zolal alphabetically, Ms. White should precede Mr. Mac because she is younger, etc... How do I further generalize my customSort function so it carries out those further criteria as well?