Can I access private members from outside the class without using friends?

If the class contains any template member functions you can specialize that member function to suit your needs. Even if the original developer didn’t think of it.

safe.h

class safe
{
    int money;

public:
    safe()
     : money(1000000)
    {
    }

    template <typename T>
    void backdoor()
    {
        // Do some stuff.
    }
};

main.cpp:

#include <safe.h>
#include <iostream>

class key;

template <>
void safe::backdoor<key>()
{
    // My specialization.
    money -= 100000;
    std::cout << money << "\n";
}

int main()
{
    safe s;
    s.backdoor<key>();
    s.backdoor<key>();
}

Output:

900000
800000