Can I Use Having My Own Health Insurance As a Bargaining Chip for a Bigger Salary?

I'm retired and will be bringing my own health insurance to any new job. Can I use that as a bargaining chip for more pay?

Suggestion:

-It might not work.
They may think you will cancell your own health insurance two or three years down the road and go with their insurance plan.
They know that you will be tempted to switch since company plans are usually much cheaper than "on your own plans".
Just mention it if you have a job offer (not before).
If you feel the pay is not high enough, you could say could I get an extra 2% a year since I will be paying my own health insurance? All they can say is no.

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