galaxys31 replied to me under the Android General and so far it seems to have worked. And yes, it was happening to both of us. Sending didn't seem to be the problem as much as receiving.
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More of a reminder than anything else: As I understand it, MMS messages cannot be sent or received via wifi; only SMS messages can be sent & received via wifi.
However, the following thread describes how one can modify the settings so as to be able to do so anyway: