You can.
Should you... is a different matter.
I wouldn't, personally. Once thawed, like meat, it shouldn't be refrozen then thawed again, and then eaten. If I wouldn't do it for my own food, I wouldn't do it with my animals.
However, I know some people do without ill effect. I say if you're going to, then make sure it's soon after a refusal (10-30min after fully thawed).
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