The standard advice is that you can freeze something a second time if it's been cooked again thoroughly in between (in this case, as mentioned above, this would mean the soup boiling for several minutes). I do this all the time exactly like you are doing for exactly the same reason: buy meat on sale when busy, and pop in the freezer; cook it up one night (roast the chicken, make a pot roast, etc.), then turn the leftovers into something else (broth or soup or a stew) and freeze it. Often it's the only way to get good value out of a large piece of meat if you are a small family. It's generally not recommended to reheat things a THIRD time, so it's best to freeze your soup in serving-size portions.

Something else to try: the "brown-n-serve" approach. Cook the half you want to freeze part way, then cool and freeze it. When you are ready to eat it, you just have to finish the cooking process. That seems to keep the cheese from becoming leather -- and the crust as well. When we make pizzas, we make an extra that is only par-baked and then frozen for later -- for those nights we just don't want to cook. When we are ready to eat it, we heat the oven to 400 or 425, and then put in the frozen pizza for 6 - 8 minutes. Sometimes we add a bit of extra sauce to the top and/or extra cheese, but not necessary. If we have the pizza stone in the oven, it takes a longer pre-heat because it takes a while for the stone to come up to temp. But it does make for a better second-time-around crust.

Meat can be defrosted and refrozen as many times as you want. Each time you do so, though, as has been said, the ice crystals that form in the cells puncture some of them and moisture will be lost. In some delicate items, like fish, you can actually turn it to mush. Very unpalatable. There is absolutely no danger in defrosting meat and then refreezing it, as long as you didn't allow it to get too warm.

It's safer to freeze it for a week than to keep it around for 4 days and eat it. If it was frozen and thawed and not left on the counter to come to room temp, I sure would refreeze it! I would refreeze it and thaw and eat within a couple of weeks. Linda C