Very occasionally on daily/weekly quests you can find a new quest in a container.
So far I have found two: "Vault 789" and "With Friends Like These".
Both gave multiple legendary rewards. Are there any more?
Fallout – How many quests can you find on other quests
fallout-shelter
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Best Answer
The Fallout wiki lists five.
So looks like I've got a few more years of daily quests to unlock them all.