You can freeze the meat again after it's been cooked. But you can't thaw raw meat, marinade it, and refreeze it without cooking it first.
Oops, apparently I was wrong! From USDA:
Once food is thawed in the refrigerator, it is safe to refreeze it without cooking, although there may be a loss of quality due to the moisture lost through defrosting. After cooking raw foods which were previously frozen, it is safe to freeze the cooked foods. If previously cooked foods are thawed in the refrigerator, you may refreeze the unused portion.
If you purchase previously frozen meat, poultry or fish at a retail store, you can refreeze if it has been handled properly.