Team admins without account owner/admin rights can access, create, modify and delete integrations, escalations and schedules only if the configuration belongs to a team that this user is admin of. However, they cannot assign these configurations into another team and they cannot convert these configurations into global.
Note that this means that you'd have to duplicate rules/integrations since the highest level of control is a single Team. Would be useful (not sure if this has the capability though) to be able to have a higher level of control over a specific subset of teams?