New job offer possibility - what visa? Currently on TN....

I am currently on TN status in the US. I am unhappy with my position and have been approached by another company with a job prospect. I am in the mid-stages of interviewing. It is an engineering position similar to my current position and I felt confident it would qualify under NAFTA. However, I just found out today that the job would require very frequent travel to 5 other countries (Brazil, Uruguay, etc). My homebase and my home would both be here in the US.

Before I proceed further in the interview process, I wanted to see if anyone here had any idea of what kind of visa situation this would require (could I do this under TN, or H1-B???). I am hesitant to speak to the company regarding the situation until I know a little bit more about if this would even be possible. If anyone has any advice or information, I would greatly appreciate it.

Why would you think that you could not do it under TN?

The travel requirements don't impact your US status. Your ability to work in other countries also would not affect, nor be affected by your US status.