Can I include in my resume that I'm working for free at a startup company in addition to my day job with my current company? How should I put it in my resume - volunteering?
If you intend to continue this extracurricular work, you will have to discuss it with your employer to make sure it doesn't violate their no-compete rules, or present intellectual property contamination issues. That's likely to hit no later than your first day on the job, when you're signing (and possibly challenging parts of) the contract. So I'd argue that if it can possibly help you it belongs in the resume... and if it can't, you're going to want to bring it up before committing yourself, possibly during the interview with the hiring manager and team.