No, it's not possible, but you can create a custom issue link type like "has subtask" / "is subtask of" and link your subtasks with it. This way you can build an parallel subtask hierarchy.
You can use "Condition / Validation on linked issues" and "Boolean condition / validator with math, date-time or text-string terms" of JIRA Workflow Toolbox to give consistency to this hierarchy and your workflows. For example, you can:
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.