@Nimo ****
yes it can be done but only on the same working day.
@Tod ********
is correct it will take coordination with your old employer and new employer. The date on the cancellation of your work permit must be the same day as your application for the new visa and work permit...(,it cannot be any other date, no excuse is acceptable). All transactions MUST occur on the same working day. If you have to travel any distance you must make sure you have enough time between cancellation and renewal.
Step 1 cancel work permit the document they give you must show work finished that day.
Step 2 Cancel Non B Visa.
Step 3 Apply for new work permit with all necessary documents. Get receipt.
Step 4 apply for new Non B Visa.
I cannot stress all dates must be correct plus all paperwork. If not you must leave the country.
I did this in May this year. It was only possible because my new ad old college personnel staff coordinated the whole process and it worked correctly. Consider the time it will take you to travel between the Labour and immigration offices at each location and how much time it takes you to travel between old and new locations.