The rishonim discuss the concept of whenever it is permitted to do one activity in a context in which it would otherwise be forbidden if it is permitted to increase the quantity of items necessary. For example, when it is permitted to cook on Yom Tov for a person's needs it is also permitted to cook extra in the same pot. Potentially this is permitted because the nature of the Torah's perspective of cooking on Yom Tov was altogether permitted and there is no prohibition at all. Alternatively, the idea of cooking a larger quantity than necessary is only a rabbinic prohibition and for the sake of enjoyment of Yom Tov the rabbis permitted cooking in a larger quantity so that a person doesn't need to define precisely exactly the minimum amount one needs to eat.
A primary source on the topic is the Gemara Menachot 64a which ponders in cases of someone who is fatally sick whether it is preferable to better to do extra melacha or less melacha but in excess quantity. The example is if the sick person is prescribed by the doctor to eat exactly two dates and there is a branch with three dates and another two branches with one date each. The given is that cutting a branch or a fruit is an equal violation of the prohibition under the category of harvesting on Shabbat. Is it better to cut the branch with three dates thereby minimizing the amount of melacha necessary to violate or perhaps it is better to cut the two branches which only hold one date each thereby yielding two cut dates instead of having one date cut unnecessarily in cutting the one larger branch? The gemara concludes that it is certainly better to cut the one branch thereby minimizing the amount of melacha. However, the implication of the gemara is that generally it is a serious consideration to try to minimize the amount of product when the amount of melacha necessary to violate is equal.
It follows that the Gemara Chullin 15b states that if a person is cooking for a deathly sick person he may not cook extra for a healthy person. In fact, even if the sick person doesn't cook extra but there happens to be leftovers the healthy person may not benefit from the leftovers.
One contrary source is the Gemara Eruvin 68a which states that it would be permitted to heat up water for a mother who gave birth recently and heat up extra water for a baby to bathe in after the milah. Our text of the gemara specifies that this is only true when one is having a non-Jew heat up the water and Tosfot (Gittin 8b s.v. af) supports this text arguing that it can't be that a Jew may cook extra. Accordingly, for the purpose of milah it is permitted to have a non-Jew do ribuy b'shiurim but, Tosfot concludes, for another mitzvah even asking a non-Jew to do ribuy b'shiurim is forbidden. However, Tosfot implies that according to the Bahag it is possible to arrive an another conclusion. 
- Ran Beitzah 9b
- Tosfot Gittin 8b s.v. af, Rashba Beitah 17a s.v. memaleh
- The Bahag (Hilchot Milah no. 8 s.v. veheycha) writes that it is permissible to ask a non-Jew to do a biblical melacha on Shabbat such as bringing a knife through a public domain in order to perform the mitzvah of milah. He derives this principle from the gemara Eruvin 68a which distinguishes between a shvut which has a maaseh and one which doesn't. He understands a shvut with a maaseh is a derabbanan prohibition in which a Jew is actively violating Shabbat, whereas Amirah Lnochri is a derabbanan prohibition in which the Jew isn't doing anything. However, the Rif (Shababt 56a) argues that this isn't correct in the text of the gemara rather it is clear that the conclusion of the gemara was that amirah lnochri is only permitted to ask a non-Jew to do a derabbanan for milah and not a deoritta. Based on the Bahag, the Rashba (Gittin 8b s.v. ve'af) writes that the next gemara in Eruvin which states that we can ask a non-Jew to heat up water for the woman who gave birth and heat up extra water for the baby is referring to a baby a few days after the milah, because if it was a need for the milah it would be permitted according to the Bahag without involving the needs of the mother. However, Tosfot Gittin 8b implies that the Bahag could have read the gemara referring to a Jew heating up extra water for the baby.