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.[core_config_data].

Step 6: Delete cache folder

Step 7: If needed give permission to media folder 777 for new server.