In my book I found this sentence...
I understand the sentence, but I had no idea such a particle combination was possible... could someone please explain it to me? Is this common?
I am surprised that you appear to find the combination unusual. も gets attached to another particle very often. It is more than common.
The sentence is saying that Ａさんの健康に関して、特にその食事に関しての心配 undermines two things -- Ａさんの心 and 家族の心. It undermines not only A's mental health but also the whole family's. This も is to emphasize the last item on the list.
Other examples of "Particle + も"