I tried to determine the manufacturer but no clues on the latch or the knob. However, I stopped in to my local True Value today and was browsing their (pathetic!) selection of hardware.
An older fella (former house builder) was very helpful when I described my doorknob and age of the house (25 yrs). He said it was probably Dexter. He said that was a very popular builders selection back in the day, but no more. We were looking around and I spotted a Schlage package called "Decorative Trim" that had just the backplate and a knob. ( It was almost as ugly as the one I was replacing :-).And it also had screws & screw holes, not concealed screws like I do.
But that gave me good search terms to use. Dexter/Decorative trim. And voila I just found online that Schlage bought out Dexter and carries a Dexter line. And Dexter has decorative trims. So I have an option. Well, maybe. Its got potential. if it fits. It's not as attractive as a whole new knob, but its cheap (Amazon carries them!) and (hopefully) it will slip right on. Could go with antique brass or aged bronze.
I will take a pic of what I've got and maybe we can determine if we think it will be compatible.