is supplementary electrode (rod) required with UFER

NEC requirements are met with the CEE.

The rod in question isn't required to meet any NEC requirements. It is therefore up to the POCO whether they want more than one rod for any reason.
In my opinion 250.52 (A) is applicable.

The rod is being installed as a grounding electrode. The purpose of the electrode is to earth the grounded conductor

250.52 (A) "electrodes permitted for grounding."
 
It’s a rod that is not needed for you according to NEC if you have a UFER. Ideas dump it’s like driving ground rods next to light poles.
You giant slab is touching acting as a GE , well I think this tinny rod will improve it.
 
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