The idea of not refreezing things has, IMHO, gotten out of hand.
If food is kept in the fridge, even if it has been frozen previously, yes you can do it.
Many of us do it when we buy shrimp at the store and freeze it. In many places it is tough to get shrimp that has not been previously frozen on the boat.
The idea behind the caveat against refreezing is that you do not want to refreeze anything that has sat at a temperature that germs like, and multiply in, and then put it back in the freezer.
You can freeze meat, veggies, or anything else, then thaw them properly and cook a dish. And then freeze that dish. The cooking will get rid of the bacteria and then the dish can be frozen with safety.
Of course, the more you freeze an item will only result in some degradation of quality.
Sorry if I seem a bit puckish this morning but it is one of my pet peeves.