I want to add additional ticket statuses for submitting tickets. Is it possible?
Yes, it is possible to add custom ticket statuses. If you want to activate this feature, see the article: Activating custom ticket statuses.
However, you can't edit or customize system ticket statuses. These are standard and they can't be altered.
If you want to add an extra level of details, consider adding the On-hold ticket status to Zendesk Support.