I take it that the goal is to list books of general interest for the software engineering student. It is not clear what the author means by classic CS material, so it is hard to know what is excluded. Surely, Mythical Man Month and GoF qualify as classics of software engineering. Or does the author mean classics from the entirety of a CS program?

I've been teaching a software engineering class for a few years. Being conscious of the high cost of textbooks, I find that Applying UML and Patterns by Larman achieves the best balance of practice, design, and process.

For students who want to dig into agile methodologies I would recommend Extreme Programming Explained by Beck and the Poppendiecks on Lean.

In my opinion, a philosophical grounding is helpful for the programmer. Accordingly, I'd want to suggest something like Locke's Essay Concerning Human Understanding or a secondary source on Aristotelian categories. Moreover, a broad knowledge of different types of ethical systems will benefit a developer.

Lastly, as a kind of curve ball, I would recommend any STEM student to work through an LSAT preparation book. Technologies will come and go, but, throughout a career, the problems a developer encounters will likely have dimensions that require general critical thinking.