If either one I see had objected to the notion, I simply would have not told them. I was not getting their permission to see other therapists and would never think it their place to give it.
I see more than one chiropractor, acupuncturist, massage therapist, and so forth. I do not believe in getting caught up in just one of any sort of health care. The few times I need bones set or antibiotics, I see the urgent care people - so never the same md either.