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:
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