What OS and version of Elements are you using? It appears that you posted a similar question in the Photoshop CC forum and it has been moved back to this forum. In any event, you will see from both threads that there are various ways to accomplish what you want.
For your particular image, I would personally use the Magic Wand tool. (Use a fairly low tolerance level, e.g 15-20 and make sure the Contiguous box is not checked.) This will select all of the white area in your image, both inside and outside the necklace.
After that, it depends on what you want to do with the image. If you simply want to replace the background color or delete the background, you can keep the selection as is.
If you want to select only the necklace, e.g. to put it on a separate layer, you can do as Peru Bob says and invert the selection (either through the Menu or via keyboard shortcut Shift+Ctrl+I for Windows) and then make a new layer via copy or Ctrl+J.
But to answer your original question, you can either create a second or additional selection by using the Shift key, or use the Add mode for any selection tool: