What is the foundational support for interpreting prophecies as having dual fulfillments?

There are a handful of prophecies that Christians consider as having "dual fulfillments" - one at the time, and one in the future. Matthew 24, Isaiah 7:14, etc. are examples. Where did this method of interpretation originate, and more importantly upon what foundation / first-principles does it rest? One could say, let's give it three interpretations, or let's say it was a failed prophecy, or let's say the original prophecy was fulfilled - but in a different way, etc. but instead Christians choose to utilize this Dual Fulfillment method on many prophecies. The explanation I've come across typically goes something like: "the first prophecy did not fully come about, so we'll see it fully happen sometime in the future." But, that's an obvious False Dilemma , as there are many other ways to explain the first prophecy not being "fully fulfilled". Would appreciate someone with more expertise chiming in.