This came up the other day.
Can a character using Radioactive clay increases the range for mind control using S.H.I.E.L.D. TA or PERPLEX? Is the range of 10 locked?

Yes.
The rule is replaced and then modify.
So is the use MC granted by Radioactive Clay you replace the character range with 10 and then modify it by +1 for every adjacent figure with the SHIELD TA.

"HeroClix Comprehensive Rulebook— updated 5.19.2021 Page 31
© WizKids 2021
13 “Golden” Rules
The HeroClix Golden Rules can’t be overruled by any effect, including those on cards that would
normally override the rules. An effect that would break one of these rules is ignored.
13.1 The Rule of Replace Then Modify
Whenever a combat value needs to be calculated, follow these steps in the order listed:
* Start with the printed value.
* Apply all replacement values that set the value to a specific number (i.e. – it becomes 6).
* Apply any replacements that multiply or divide that value (usually halving or doubling).
* Apply the sum of all modifiers (+ and -)
If there are multiple replacements of the same type, the active player decides the order. If the result of calculating any value (combat or otherwise) is less than zero, use zero instead."

Note that if Radioactive Clay said, Minimum Range of 10 the value couldn't;t be modified as minimum values are not replacement values,, nad will not be modified unless otherwise stated (see example wkMP19-s109 The Liar).