What are the steps to upgrade my non-b work visa for multiple entries in Thailand?

You GO apply for your yearly extension at the immigration office for 1900baht.

Sometimes Non-B extensions get a 30 day under consideration stamp (meaning you go back after 30 days and get the year extension inked in) but sometimes the year is issued on the spot.

You apply for the extension and then you buy a re-entry permit, a single re-entry is 1000baht and a multiple re-entry is 3800baht. They are stamped in while you wait.

Remember the re-entry permit stamp is valid as long as your current stamp is good for

So if when you apply for your year extension you get the 30 day under consideration stamp any re-entry permit you buy will be good ONLY for that 30 day period and after you get the year extension inked in you'd need to buy a new one.