1928, Escutcheon, for exterior door handle

The exterior door handle escutcheon. 
The base of an OUTSIDE DOOR HANDLE for cars from the late 1920's
 This is the little dohicky that HOLDS THE HANDLE TO THE DOOR.

Fits Marmon: Model 78, Model L, Little Marmon, Big 8??

The Handle (sold seperately) locks into this Escutcheon with a 3/4" retaining ring.
The escutcheon screws into the body with two screws.

These might have been purchased by Marmon from an outside vendor that also sold them to other auto manufacturers.  If they look like yours, buy the plastic samples and see if they fit.  If you like them, purchase the steel versions.

The original mechanism was made from pot metal and swelled with age. 
The handles were often held onto the escutcheons by peening over the soft metal of the handle so that it folded over the edge of the escutcheon.  When the pot metal swelled, the handle locked up.

These redesigned assemblies are held together with common retaining rings, making them easy to take apart to clean and lubricate in the future.
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Buy the plastic version to test for fit before comitting to the expense of the steel version.
If you are low on cash and NEED a handle, you can just paint the plastic parts and see how long they will last.
With gentle use, they may last a while, but if you have the money, get the steel.
I do not think that the plastic version would be strong enough for regular use by your passengers.
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Please note that the retaining ring and screws are not included.