Remote Work - Tax Question

My girlfriend is an occupational therapist and is heavily considering signing a travel OT contract for the next few years as the pay is pretty wild right now.

My current job switched to remote in March 2020 and apparently it is going to be a permanent change. That being said, most of the office is based in the NOLA area, other then one guy who lives in Chicago and our President who lives in BR. I have not discussed the possibility of working remotely to this extent with them, but for the sake of argument we’ll assume they’ll allow it.

I understand that you would typically be paying state income taxes where you are residing while the work is being completed and not the state that you have as your permanent residence or where the company is based. Realistically, if I am moving every 2-3 months will I need to file with every state I have been in? Or can I get by with just filing in Louisiana? Is HR required to withhold taxes for different states as I move, or would I just receive a full refund from LA and owe to the other states I lived in?

It seems like people that travel frequently for work would not need to do this, so I feel like there is some work around or exception that I’m not aware of.

Any advice or corrections to the above would be appreciated.