Methods and apparatus for supporting switching of data paths corresponding to a communications session between different non-3GPP access networks, e.g., networks including WiFi access points, using network core functionality are described. This allows a communications session in which a UE is involved as an end point to be switched between two different WiFi access networks and/or a WiFi access network and a 3GPP access network, e.g., cellular access network, without the communications session being terminated while service is provided to the UE by a Public Land Mobile Network (PLMN) with which it is registered. A UE can switch between multiple WiFi networks while maintaining a communications session supported by network core functionality even though the session may be switched between different non-3GPP networks while the session is ongoing.