Is it possible to store a received call?

I think you can only do it if you manage the calls from withing your app (VOIP).

I don't think anything changed since this old thread (except reinforcing privacy protection):

https://stackoverflow.com/questions/4003791/programmatically-get-the-number-of-the-incoming-call

Otherwise, you cannot get info on "general" calls (for privacy reason, as that would be a way of spying telephone).

This thread talks about how it isn't possible. I am trying to develop an app that displays the call history an infinite number of calls since iOS only allows up to 100 calls. Any ideas?

Send a feature request to Apple, and wait. Though, call history is a very private thing and Apple would not provide such features.