Use the following steps to move Magneto Multistore from one server to another server  :

Step 1: Collect all backup and database of Magento Multistore from old server.Step 2: Create new data base for Magento Multistore on new server.
Step 3: Transfer Magento Multistore files to root path.
Step 4: Apply basic configuration through data base and xml in new server.
Step 5: Apply sub store wise configuration through data base in table i.e.
Step 6: Delete cache folder
Step 7: If needed give permission to media folder 777 for new server.