It appears as if the Samsung S4 will not complete a send or receive of an MMS while attached to wi-fi; this requires mobile data be active and consumer data usage in order to work. If this is correct, it seems that this is a network as well as software requirement intended to increase data consumption (cost $$$). This is also a true statement reguardless of any extended MMS program to which you may currently subscribe. I have attempted to get Verizonwireless to respond, but their customer service department seems to be overloaded.
Again, if the above is true, this makes new and expanding SPRINT and AT&T alternatives more attractive.