Establishing Web/Operations Engineering in mid-size SaaS?

HN, I work for a growing ~200 employees SaaS company where up until now the "tier 3/4" support team is responsible both for supporting all application related escalations and "supporting" the system itself - i.e owning up-time and performance. I now have an opportunity to restructure this into a more sane division of labor but I can't find any literature on the subject to help model it. I want to be able to clearly show that the people that are resolving tickets regarding bugs in the back-office accounting app should not be the same people debugging stuck threads on the application server and optimizing DB queries. Any thoughts?