Yes, you can start over. However, it is best to use one account only. This will ensure you are able to access prior returns and that your information is transferred over into your new return. Use the account you filed with last year (If you used Turbo Tax). Now, if this is the account you are using, you can start that return over. If it is rejected again, you can fix it the error and continue to file.
This FAQ will show you how to fix a rejected return. https://ttlc.intuit.com/replies/3302275
This article will provide information on Clearing & Starting Over after you've registered.https://ttlc.intuit.com/replies/5647695