JR Shinkansen train, ever a supplement?

Planning on buying a JR 14 day ticket though working on ways to either not active it or figure a way to get a 7 day pass. I got to wondering if there would ever be a supplement for a JR Shinkansen train with someone holding a JR Pass? I know there are private lines but I would try to be on JR Rail lines and JR Trains. TYIA

Flying

Your question is unclear. Are you trying to travel cheaper - cut down long-distance travel to fit within 7 days instead of 14? If you post an itinerary you will get clearer options for this.

Some trains do require a supplement for JR Pass holders, as they use tracks owned by non-JR companies. These are uncommon and listed in the JR Pass details.

I got to wondering if there would ever be a supplement for a JR Shinkansen train with someone holding a JR Pass?
Short answer - no.
Longer answer - The class of pass allows you to ride in the class designated and the ones lower. A green car pass allows green, ordinary and non-reserved. Ordinary pass for ordinary reserved seats and non-reserved.
I do not think you are looking at upgrade options to Gran-class or from Ordinary to Green which are very expensive.
All shinkansen lines/tracks in Japan are covered by the national JR pass - there are no private shinkansen routes.

Agree that your question isn�ft very clear. If your question was if you can pay a supplement to travel on Nozomi or Mizuho trains (the fastest, most frequent) the answer is NO. with no JRP you can use them.