Can I activate a TN for my new job before I quit old one

Hello,

I have given notice at my current company in the US and would like to activate the TN for my new company before my final day at the current one. Is there any issue in holding 2 full-time jobs with 2 TN visas at the same time?

i.e. will CBP give me trouble for technically holding 2 full-time jobs at the same time(eventhough it will be for a week or two)?

This is no problem

In fact, you would havebeen safer to get your new TN first, and THEN quit your old one, just in case you are denied new TN.

Thank You for the response.

Do I have to say anything at the border when activating the new TN or do I not have to worry and just state that I have another job and show supporting documentation?

I would probably mention the current TN, as this expalins why you have a US DL and plates, but make sure that they don't lift that I-94: you need it until you wish to stop working at Job A.