I honestly would love to keep them but many of the pulls are broken and the cost to fix them would be much higher compared to replacing them.

If I were going to change them out, I would probably look for a large backplate which would allow me to use whatever knobs I preferred. This is an example of what I mean:

Anvil Mark 2491930 Knob and Backplate, Satin Nickel, 2-3/4" Diameter, Set of 5 · More Info

Wow, excellent idea. Thank you Mary!

I vote for identical replacements.

I'm suggesting spray painting the original hardware to whatever color you want. There are some gorgeous metallic spray paints out there and that is what we are doing to the 42 year old dresser that we are going to refinish. I also thought about replacing the original hardware but my hubby took one of the handles off, cleaned it, and sprayed it with silver metallic paint. What a huge difference!

Do you plan to do anything to the wood? Paint? Refinish? If not, rub it down with Murphy's Oil Soap to refresh the wood and keep the pulls that are there already. The original pulls look to be in better shape than the wood does.

Who knows, you might run across "just the right pulls" someday.

You would not be "updating" the chest but making it look very VERY odd. That style of dresser is meant to have those very knobs and anything else just looks wrong. Suppose you had a very simple Danish modern teak chest and put on Chippendale batwing style pulls? That would look as odd as "updated" pulls would on that chest.
And don't ever use Murphy's Oil soap on anything but maybe your kitchen cabinets....certainly not on fine furniture....it will cloud certain finishes.

OK, Murphy's wasn't what I was trying to remember. It was Lemon Oil but in searching for that I found that coconut oil would be even better. Just plain coconut oil like you'd cook with.

One other tidbit, Architectural Digest recommends Murphy's Oil Soap.

Thanks everyone for your input! I decided to replace the pull rings (which are all broken by the way) with the same type of hardware The ring is 2 1/8" in diameter and it was really hard to find a replacement for but I found one and will post an updated picture once I have them on. I ordered all new replacements for the matching tallboy as well.