We are hooking Features into Epics, and discussing with development and the rest of the product team, the individual enhancements, new features, and tasks that are required to be performed for the "Epic" to be completed. Aha/Jira integration only allows mapping one type of ticket into requirements, where we'd need a few different types since Development makes these tickets from Jira.
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The best way to achieve this would be to create multiple integrations. As you had noted, each integration allows for 1 mapping. By creating multiple integrations, you can send your features/requirements to JIRA via the correct integration set up.