Can I reuse boiled chicken bones to make more broth?

I recently made pozole. So I boiled 5 little Cornish hens until they were cooked. Took them out to shred the chicken and then threw away the bones. I ended up with more broth then I needed so I froze it which got me thinking. Could I have saved the boiled bones to make another broth? If so, how many times?

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