Yes. Word calls this "versioning". One file will contain all the versions and will increase the file size. You can also extract any version and save it as a separate file. To use the version options:

1. Choose Versions from the File menu.

2. Click the Save Now button to save the current state of the document. Word records the author and the time and date of the version. You can also add comments to distinguish each version.

If you check the Automatically save a version on close, Word will do just that. You can still use the Save Now option to save other versions of the document. To view your version history:

1. Choose Versions from the File menu.

2. Select a version then click on the Open button to view that version in a separate window.

3. To keep a particular version, use the Save As command on the File menu.