Hi Laura,
As far as I know, in the current Photoshop CC 2017.0.0 version there is not a way to do exactly what you are looking for.
I am assuming you're looking to save a JPG?
There is a checkbox in Photoshop's "Save As" dialog to save as a copy. It leaves your original file as is and appends "copy" to the new filename. But, this involves changing the file format to JPEG. I believe it defaults to PSD.
You could also use the Export method in Photoshop. You can choose to have "Quick export" always save the image to an "Assets" subfolder to what you are currently working on, or in "Export preferences" you can set it to always ask you where to save the file. In that case the folder will default to where the current file is. In that case, when the Dialog comes up, you would just press right-arrow then 1 or A or whatever you like. ("Quick export" is what I use myself)
I hope this helps.
-Mick