Can I change my visa extension from employer-based to marriage-based while keeping my job in Thailand?

just go to your local immigration and ask

You need to convert your visa from a B work visa to an O marriage visa. You cannot extend a B visa by reason of marriage.

Work Permit is tight to the job and is from the Ministry of Labor.

Your Extension of Stay is from the Immigration Office, two different things.

You can change the reason for a new Extension of Stay into based on marriage but you need to meet the financial requirements;

OR 2 months 400.000 Thb on a Thai bank account on your name or a minimum income of 40.000 Thb a month.

If this income is made in Thailand proof of SSO and Tax payments from you and 4 Thai staff are needed over the last 3 months before application.

As for extension-wise, changing the reason from employment to marriage to a Thai is not a problem. You can use your salary income as proof of your funds. Being an extension based on marriage to a Thai is no problem for you to keep your work permit.

But, how it would go depends on your employer. You may need the letter from your employer saying agree to change the reason. You also may need some documents from your employer to prove your income, just showing your payslip may not be enough.

You better go to your local immigration office to get a handout of requirements for a 1-year extension based on marriage to a Thai first. Then check what you need, and talk with your employer to be sure they and you don't have any problem to change.