Can you apply for a multiple entry Non-B visa in Bangkok if you already have a work permit?

Nope

There is no multi-entry visa of any type available inside the country at an immigration office.

Depending on your employer and the documentation they provide, you might be able to go to the immigration office and apply for a 90 day Non-B visa. Once you get that, you can apply for a yearly extension of stay and then after that IF you needed a re-entry permit you could buy one of those too.

IF you're looking for a year-long multi-entry Non-B (the kind where you border-bounce every 90 days) you need to go to a thai consulate to get one.