Studying a second undergraduate degree part-time while doing a PhD?
If it does not interfere with your graduate studies, then no one could possibly object. People should have hobbies outside their PhDs, and if you a Physics student has an interest in Classic Philosophy, then so be it.
But you need to be sure it won't interfere. There is a world of difference between taking the odd evening class in something and enrolling in a degree, even part time. Think about how much time you have: Our full-time undergraduate degrees are designed to require 37 hours a week of study. Even doing such a degree over 5 years, rather than 3, you would still be talking about 23 hours a week. Are you going to manage to be working at peak performance if you are doing this on top of 40-50 hours a week of graduate study?