H-1b transfer after i quit (to anothr h01b or tn-1)

I'm a Candian citizen (born in Canada), and have been in the US on a h-1b that expires in October of this year. Originally I was here on a tn-1, before i got a h-1b.

I quit my job with my US employer then I found out another US company was interested in me. I will likely get an offer from them the week after I stop working for my old employer.

Can i still transfer the h-1b visa to my new employer? Will my new employer (and their lawyers) have troubles doing so?

If I can't transfer the h-1b can i get tn-1 status again?

If you transfer on H-1B, you're only allowed the time left you could have gotten with your original employer and there are other restrictions as well, iirc, I think you still have to meet the job advancement criteria.

If you're in a NAFTA job category and qualify for TN-1, it's the simpler route I would say. The only reason to stick with H-1B is that it's a bit simpler for them to sponsor you for LPR status.