As I'm starting to look to put together my plan of study, a question popped into my mind: are there, generally speaking, rules against taking additional courses beyond what is required for a Ph.D., or is it simply frowned up by most advisers (in the interest of creating more time for research endeavors)? I ask because I've found several graduate certificates offered at my university that seem relevant to my interests (in teaching), and I'd like to take an additional 2 or 3 courses to fulfill their requirements. I've heard from other grad students in my lab, however, that there is frequently push back from our adviser on such matters.
As an adviser, I encourage my graduate students to take classes they find interesting and/or that broaden their knowledge and therefore are useful to later finding jobs. Ultimately, my goal in this is to help my students become well rounded and broadly educated graduates who will be successful in life. The only caveat I place on this is that they need to make sure they have enough time to do the research that will ultimately lead to their thesis and their defense.
I don't know whether I'm typical in this, but would imagine that most advisers will agree to let their students take other classes if a student asks and gives a reasonable justification. I think most will even agree to this if the student is paid from a grant.
Taking extra classes is a great idea, but be sure to check the financial aspects of your plan. As far as I know, teaching assistantships in my department come with a tuition waiver that covers only a certain number of classes (especially after you've passed your preliminary exams and are supposed to be working on your thesis); if you sign up for more classes, you might have to pay tuition that you weren't expecting to pay.
It's quite common to take courses beyond the requirements just because the material is interesting to your or because you think it will be useful in your future career. However, at a certain point, it will become clear that it is time to focus on finishing your dissertation which after all should be your top priority. You should discuss this with your academic advisor.
I'd be in favour of taking extra classes. But be careful not to spread too widely, in the end, you'll have to select a line to specialize in. There are many, many subjects that intrigue me; most I have to let pass with regrets.
Whatever you do, check with your advisor if that is how the environment there works. Perhaps talk it over with people in the group, or some other person you trust. For me, the fact that you are troubled enough to ask here is a sign that you should think it over with some help.
If your have enough time and you are keen to take additional courses apart from your coursework subjects, then you can take them. I took two additional courses during my PhD. It helped me in many ways, e.g., I could sharpen my knowledge in my field, I could mention these subjects along with my coursework in my application for Post-Doc positions, etc.
It's ok to take extra courses to support your PhD or just out of personal interest. I took a graduate certificate myself which lasted a year (as a part time course) whilst doing my PhD which I found very helpful. This was more relevant for me because my research is very interdisciplinary requiring skills from multiple fields. However, a note of warning: it must not get in the way of your PhD-this is after all your primary focus. It's a good idea to do any course that will require some commitment from you in your first year of PhD because you're likely to get very busy towards the end of it. Generally speaking, you won't be able to take too many due to financial implications and in order not to get too distracted from your PhD.