In Photoshop Elements, choose File > Process Multiple Files. This opens the Process Multiple Files dialog. Select the destination folder for the resized images (you can create one from this dialog), or, if desired, select Same as Source. Edit the images and save them in available formats with the edits.
I think you mean that after editing a number of photos in your photo bin, what you want is to 'save all' and your choice is only to use the 'save as' option which asks you to confirm the output name and option for each file successively.
I don't know any way to do that from Elements.
I think that the very affordable external add-on Elements+ offers a script for that: