K.P.
I had my platinum engagement ring resized and it was fine. It's a plain band, so it may have been easier as a result, but it wasn't overly pricey and they had my rings for a couple of days. My uncle is our jeweler and when we bought my wedding band, he insisted that we not have diamonds on the bottom for this very reason! According to him, as long as there are no stones on the bottom, the ring can be resized.