Too much Vitamin C is also bad. So I guess, in answer to your question, I guess it is possible to have too many fruits and veggies. ;)
Would that really be having too much though? I don't remember any other negative effects besides discoloration of the skin, but is that really so bad to consider it to be too much?
Well, I know different vegetables contain different chemicals. When I used to take boxing classes, someone told me that if I ever started to do veggie smoothies that I should have a lot of variety and rotate the vegetables I use to reduce the risk of alkaloid buildup. I'm not a nutritionist, so I don't know if that's actually a thing or just bro-science.
My research says that alkaloid buildup is in fact a reasonable concern, just in case you were still curious about it