Disclosed is a method performed by a first core network node, for enhancing service continuity between a wireless device and a second network via a first network, wherein the first core network node is part of the first network. The method comprises receiving, from the wireless device and/or from a second core network node of the first network, control signalling indicating that the wireless device requires that a tunnel between the wireless device and the second network and via a gateway of the first network is maintained. The method comprises controlling a radio access network node and/or the gateway based on the control signalling and a capability of the first core network node of the first network to maintain the tunnel.