If you’re applying for permanent residency and want to change jobs during the process, there’s a range of answers. Without knowing more specifics about your particular situation, it’s difficult to provide an accurate answer. So, the general answer (which is not a legal opinion) is that it’s possible.
Where you are in the PERM process is going to determine much about your eligibility to switch jobs. If you’re in or near the last phase of the process, your Form I-485 application has been pending for a minimum 180 days, and your new job is in the same or similar occupation as your original job, then you probably can change jobs.
This area of law is extremely tricky and noncompliance can result in penalties. You should really consult an immigration attorney who can ask you the right questions. We deal with these questions all the time at, a site I developed to help people get quality legal answers fast and inexpensively from top-notch lawyers. Check it out for more information or PM me directly with any additional questions you have. I hope this is helpful!