What is considered “a case of need” when it comes to violating a double rabbinic prohibition?

Question

A shvus dshvus (rabbinic prohibition on top of a rabbinic prohibition) is allowed במקום צורך (in a case of need). But what is considered במקום צורך? And is a shvus dshvus allowed for anything besides במקום צורך and the performance of a mitzvah? If so what?

EDIT-for those who want to know what a shvus dshvus is, the Wikipedia link רבות מחשבות gave has a pretty good explanation. As for how I know it's allowed for mitzvah, sick people, and great need, the Wikipedia page says that the Rambam says it (Hilchos Shabbos 6:9). Additionally it mentions it in the 39 Melochos book by asking a non-Jew to do a drabbanun (rabbinic prohibition). And I've seen it a lot in the Gemara (like Tosfis explaining why Rebbi Yehuda would allow first sex on Shabbos since it's destructive. It's somewhere in Kesubos (5b s.v. "Im").

Answer 1

It must be a big tzorech that would cause great anguish if not done, like: a loss of significant money(except a fire; see SA OH 334), not having food to eat on shabbat, public embarrassment, and problems to physical or mental health.

Answer 2

One example (among many) that illustrates the concept of במקום צורך is found regarding the laws of giving out Aliyahs for Krias Hatorah:

The Rema in Shulchan Aruch (Orach Chaim 135:10) quotes an opinion that although we are accustomed to not call up a Kohen or Levi for the other Aliyahs (ie. From the fourth through the seventh) however the Rema rules that after all seven Aliyos have been fulfilled, one may call up a Kohen or Levi. The Rema ends off saying that this is the custom. However, במקום צורך one can rely on the first opinion (the S”A’s that is it permitted to call up Kohanim and Leviim even within the first seven)

The Mishna Berurah (ד״ה במקום צורך ודחק):

כגון בשמחת תורה וכה"ג יש לסמוך דמיד שקרא ג' קרואים הראשונים כהן לוי וישראל מותר לקרות אח"כ כהן או לוי וכמ"ש לעיל בדעת המחבר

The Mishna Berurah says that an example of a במקום צורך is the custom on Simchas Torah to call everyone for an Aliyah - we add to the amount of Aliyos that is generally read.

This is but one of MANY examples