As long as your local immigration office sells that type of in-country Non-O and your employer can provide all necessary papers for that, he can apply for in-country Non-O dependent to a foreigner who is working in Thailand legally. Have your company HR person talk to the local immigration office for the latest requirements. The documents to be submitted are immigration-office-specific.
Here is the general information, which cannot be guaranteed as the latest.
*********************************************************************************************************************************
*******
/4.FOREIGNER-WHO-IS-WORKING-IN-A-COMPANY-OR-LIMITED-PARTNERSHIP-NON-O.pdf