Q: Can I change my Apple ID & personal email address and have a business email address also coming into my Mac?

You can make a second email address for you business needs. You do not need another Apple ID for it, but you may prefer to create one to use only for your business.

As for your current Apple ID you can make changes:

For Problems With Your Apple

 

1. Forgot iCloud Password
2. Forgot Apple ID
3. Apple ID - Apple Support
4. Manage your Apple ID primary, rescue, alternate, and notification email addresses - Apple Support
5. About your Apple ID email addresses - Apple Support
6. Get help with Apple ID

Be sure you know the answers for your security questions. If you have forgotten them:

Forgotten Security Questions

 

1. If you forgot the answers to your Apple ID security questions - Apple Support
2. Apple ID- All about Apple ID security questions
3. Contact Apple for help with Apple ID account security - Apple Support
4. Security questions

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Yes, see:

http://www.apple.com/support/appleid/manage-account/