It is possible to easily upgrade plesk 9.x to plesk 11.x. However, it can cause issues and need not be a very smooth process. It can break things at times. If the upgrade does not complete smoothly, we will have to troubleshoot broken upgrade and it can cause extensive service down time as well.
So the safest option to get plesk 11.x, will be migrating websites to new container/server with plesk 11.x. Once the new container is ready and migration has completed, we would request your to verify whether all the domains and settings have been migrated properly. Upon receiving your confirmation we would change the DNS so that your domains would point to the new server.