If the remaining tile is in good shape and not falling apart then you can overlay it with a polymer cement overlay and even color and stamp it like stamped concrete.
This overlay only needs to be 3/8 of an inch thick and will be very strong and durable.
If there are more tiles that are loose, they can be removed, do any repairs to the existing stairs and porch with a polymer cement or a product from Rapid Set called Cement All. Then you can re-tile over this material also.
I think the stamped concrete overlay would be a great option if you can find a good installer.