Supererogatory actions are admirable but not obligatory. A sufficient, and perhaps necessary, condition for an action A to be supererogatory is that (a) A is permissible and (b) there is an alternative B to A such that (i) it is permissible to do B instead and (ii) A is more morally praiseworthy than B.
Over the years, I've met people--including myself--who have been troubled by the idea of supererogatory actions and tempted to deny that there is such a thing as supererogation. But here is a pretty conclusive argument that there can be supererogatory actions. You and your friend, both innocent people, are captured by a tyrant. The tyrant sentences your friend to 24 hours of torture. Then the tyrant offers you the option of reducing your friend's torture by any amount of time less than 12 hours. And of course, she notes, any torture taken away from your friend will be given to you, by Public Law Number One: the Preservation of Torment.
Now, many people will say that any taking on of your friend's torture is automatically supererogatory. But I think the sort of people who doubt that there are supererogatory actions won't be impressed--they tend to have a view that morality does indeed sometimes call us to very great sacrifices (and they are right about that, even if they might be wrong about this case).
However, the following is surely true: There is an amount T1<12 such that it is permissible to reduce the friend's torture by T1 hours. Indeed, surely, T1=11.99 qualifies. (Argument: reducing one's friend's torture by 11.99 hours, given the cost that one will suffer that torture oneself, is plainly praiseworthy simpliciter, but only permissible actions are praiseworthy simpliciter.) Let B be the action of reducing one's friend's torture by T1 hours. Let T2 be a number such that T1<T2<12. Let A be the action of reducing one's friend's torture by T2 hours and let B be the action of reducing one's friend's torture by T1 hours. Then, barring further factors not given in the story: (a) A is permissible (it would be odd if it were permissible to reduce one's friend's torture by, say, 11.99 hours but not by 11.999 hours); (b)(i) B is permissible and (b)(ii) A is more morally praiseworthy than B. Thus, A is supererogatory.
If you think time is discrete, the above example still can be made to work. Suppose for simplicity 11.99 hours is the longest time interval short of 12 hours. Then if you think there is no supererogation, you might think that you're obligated to request that your friend be relieved of 11.99 hours of torture. But as long as the agent in the story doesn't know that 11.99 hours is the longest time interval short of 12 hours there is, she can do something more praiseworthy than requesting the 11.99 hour reduction: she can request 11.999 hours, and as long as she is not certain that 11.99 hours is the most she can get, she thereby risks getting more than 11.99 hours of torture as the cost of trying to relieve more than 11.99 hours, and that's more praiseworthy than just going for 11.99.