The Third Generation Partnership Project (3GPP) Fifth Generation (5G) networks employ network slicing in order to implement multiple service types corresponding to different business needs. Network slicing results in the creation of multiple end-to-end logical networks over shared physical infrastructure. User Equipments (UEs) can use multiple network slices concurrently in order to avail a diverse set of services. In order to support UE slice mobility, especially for UEs accessing multiple slices, 3GPP mandates that all supported slices should be deployed homogeneously within a Registration Area (RA). However, studies have shown that the deployment cost of the network increases with the increased number of slices. This makes it a costly proposition to deploy all supported slices on every Radio Access Network (RAN) node within the RA. In this paper, we propose that the slice deployment requirements can be more flexible while ensuring UE slice mobility through the use of an enhanced multi-connectivity protocol. The proposed protocol can also be used for ensuring slice mobility across multi-Radio Access Technology (RAT) networks, including 5G New Radio (NR) and Wireless Local Area Networks (WLANs). The performance improvements obtained due to the proposal are demonstrated through simulations in network simulator-3 (ns-3).