Respectful freeist
If a "Respectful freeist" had the same amount of true-care as a freeist, he would be quite "self-sacrificing", because these people have natural-respect too. As you can see from the diagram below.
On the other hand, if a "Respectful freeist" had less true-care and natural-respect, but it still added up to be equal to their self-interest, (let's say a morality of (1, -0.5, 0.5)) he still would be innocent, and much like a freeist, except that he would be less likely to help innocent others for the sake of it.