I’m not sure I fully understand your question here. Can you provide some code examples of the issues you are facing?
It’s usually quite easy to adhere to SRP providing you’re using Dependency Injection correctly and not Digging into Collaborators
Correct me if I’m wrong but you’re acting as if the “Domain model” is a single object within the system? (Or perhaps a single object within a specific MVC triad? either way…) that’s not the way to think of it. The term “domain model” never refers to a single class but any number of classes required to represent the domain (In simple scenarios it can still be one, of course)