I didn't have anything helpful to say. I've done side projects when I was working for Big Corps, but in every case notified management beforehand and got a written ok. Never had any trouble with it. When I've accepted job offers, I'd also provide a list of projects that were mine and had them sign off on it as a condition of employment. Never encountered any resistance to that, either.
But these poor people were sweating bullets imagining all the bad consequences of their employer finding out.
Just ask, in advance. If you're a valuable employee, they'll say ok. Never heard of one saying no. And they'll appreciate that you asked instead of sneaking around.
But be careful not to use company equipment.