The Halacha allows instructing a non-Jew to do a Melacha D'Rabanan (Shvut D'shvut) for the purpose of a Misva. The question is whether this is permitted even if the Misva will not be accomplished until the next day? For example, if the first night of Pesah falls out on Mosa'eh Shabbat, can you tell the non-Jew on Shabbat to go outside the Tehum (Shabbat Boundary) to get the Massot for Mosa'eh Shabbat?
There is a big debate regarding this. Maran in 307:5 discusses a case where it is permitted to tell a non-Jew to climb a tree on Shabbat to get the Shofar. Telling the non-Jew is a Shvut (Rabbinic prohibition); climbing the tree is a Shvut and the Shofar is a Misva. However, the Shofar Is not a Misva for, because we do not blow the Shofar on Shabbat. The case must be that they need the Shofar for Sunday, and yet Maran says that it is permitted. It seems from here that Shvut D'shvut for a Misva for the next day is permitted. That is the way that some of the Poskim learn Maran. However, other Poskim, like the Tur (R. Ya'akob Ben Asher, Germany-Spain, 1269-1343) leave out the word ‘Shabbat,’ implying that the case is talking about getting the Shofar on the day of Rosh Hashana itself. Therefore, it is Bo Bayom- for that day. It could be that Maran only used the word ‘Shabbat’ because that is the wording of the Rambam, but really, he holds that it is not specifically Shabbat. The Poskim go back and forth, debating why Maran would write ‘Shabbat’ if he did not really mean ‘Shabbat,’ and actually meant on Rosh Hashana.
Practically, Hacham David in his Halacha Berura, (p. 209, Siman 307) writes that one should only ask a non-Jew to do a d'Rabanan for the purpose of a Misva the next day if there is a pressing need, such as the possibility that if he waits until tomorrow, he may not be able to fulfil the Misva.
One may instruct a non-Jew to perform a Rabbinic prohibition on Shabbat for the sake doing a Misva after Shabbat, if there is a chance that otherwise, he may not be able to perform the Misva at all.