Many airlines will be happy to allow you to travel with as many as 10 cases each, though of course you will have to pay a considerable amount for luggage over and above the luggage allowance of your ticket.

The exact answer to your question will depend entirely on the airline you choose, and the type of ticket you buy.

If you have lots of luggage/items to transport, you may be better off having your luggage transported by a specialist freight/moving/luggage forwarding/courier company rather than carrying it all yourself.