Can I change my job while in Thailand on a non-B visa without leaving the country?

It can be done I have do this myself a few times,

1. however both employers need to Co ordinate this very carefully and work together

2. Typically this only works if both employers use the same immigration /DOL office for new and old WP

3. If it's inter-provincial it will easier starting over gets too complicated

The times I have done this it's been via the BOI in BKK as all companies are BOI companies

It is possible to do inside the country, but that depends on both your employers as the immigration office(s).

You need your old employer to coordinate with your new employer as well as the immigration office for both your old and new employer.

You would need your old employer to cancel your work permit and you cancel your work extension based on your old job, and then you would need to go to the immigration office of your new job with the paperwork from your new employer to apply for a new work extension based on this new job. It's a lot to coordinate, and all of these parties have to agree and work together to make it happen.