For a spherical mirror, an object at the mirror's center has an image that is also at the center. Its magnification is $-1$. For a video showing this, see here.
If you stand slightly behind the center of a large spherical mirror and hold out your right hand, as if to shake, you will see a reflection of yourself, upside down, holding out its left hand. You can "touch" palm-to-palm with the reflection, or pass through it, but your hands won't be the in the "shaking" position. Instead, the thumbs point opposite directions.
Is it possible, using any combination of mirrors and lenses in the geometric optics limit, to create an image at the same location as the source object, with magnification $+1$, so that you could appear to be shaking your own hand? As you hold out your right hand, your image would need to appear right-side-up and also hold out its right hand.
Here is a faked picture of what I'm thinking of. To make it , I photographed my own hand, then used a computer to copy my hand, rotate it 180 degrees, line it up with the original, and "ghost" it out a bit.
There is no requirement that the image hand track yours if you move around - a static handshake is enough. I don't necessarily have to be able to view the image directly from where my head is, but it should be a real image so that if I make the air dusty, someone watching my hand from any angle would see the image.