The functionality that you described is not currently offered. You can, however, run multiple Response Plays in any order you wish manually from both the web and mobile applications. You can also store a runbook against your services within PagerDuty, so your responders have reference for which Response Plays to run and when , and in what order.
Building a Response Play workflow like you described is certainly something that PagerDuty wants to explore in the future. If we begin deeper discovery on such a feature, would you be interested in participating in an interview with members of our Product and UX team?