Multiple policies covering same risk?

I half overheard a conversation in my agency (where I do accounting work), about an insured "double dipping". I didn't get the context or resolution to that situation, but it did beg the question for me --

Is someone allowed to have multiple policies from multiple carriers, covering the same risk? (A car, in this instance)

I could see both sides, in that presumably the insured is paying both premiums and is in good standing with both companies, but it also seems like something the carriers would kick up a fuss over.

Is that legal / allowed? Is there a hidden risk to it?

Edit: That makes sense!! Thanks everyone!!