Can users include multiple shipping adddresses /edit the field to include the address at the time of purchase? i mean, if one user (say a company) has multiple locations where it would like to receive its orders, is it possible to add multiple locations, that will be registered?
Yes, you can have multiple shipping addresses and edit them.
You can test that yourself in one of our test stores:
Simply log in and you can go to My Account > Addresses to edit. You can also submit a test order and test editing the shipping address in the Checkout. The only requirement to be able to edit the shipping address on Checkout is being authenticated.