Yes, by mail.
In that case you can ask that your replacement document be sent to an address that is different from the address on your document. You can't have it sent to a different address when you order online.
What if I want my non-driver ID to be sent to that address too?
You'll have to include an additional note and clearly print the alternate address. Don't write the alternate address on form MV-44. The mailing address you write on form MV-44 must be the address that is listed on your photo document and your DMV record.