To date, mobility and multihoming support in IPv6 have been considered independently of each other, which lead to the publication of the standards Mobile IPv6 and Shim6, respectively. Nevertheless, several use cases that we show prove that there is a strong interest for simultaneous use of these two protocols. In particular, the combined solution allows for replacing the routing optimization mechanism of Mobile IPv6 with a lighter technique, equivalent in functionality, without needing to extend the already defined protocols. We also provide an evaluation of our architecture, based on our publicly available implementation for Linux