With a phrase like "More than once", it's the nuance that is important, not the actual number. It's meant to be a contrast with "Only once". You use this phrase to emphasize that you have done something more than one time, but want to be ambiguous about exactly how many times.
This is why, in your example, it can be funny when properly phrased:
I know they must have had sex more than once in their marriage -- after all, they have three kids.
The evidence suggests that they had sex "more than once", but the joke is the implication they had sex only the three times required for procreation. Since the number is ambiguous, the listener has to "get" the inference.
Again, as with many ambiguous number-related phrases in English, the actual number doesn't matter. Possibly you want to imply something, like it is larger number than it actually is:
A: I know Europe really well. I've been there more than once.
B: Really? How many times have you gone?
A: OK, you got me. I've only been there twice.
Or, possibly, it's been a lot of times and you want to downplay the actual number.
He's been down this marriage road more than once. By now you'd think he'd have figured out he's happier being single.