How should I go about collecting exceptions and putting them into an AggregateException to re-throw?

For my specific code, I have a loop and will have zero or more exceptions thrown from a part of the code. I was hoping to just add the new exceptions to the AggregateException as they arise, but the documentation sort of indicates that it should be constructed with all the Exceptions at once (there is no method to add an Exception to the object).

And what about creating a new AE every time and just including the previous AE in the list of exceptions? Seems a hokey way to do it.

Any better ideas?