Currently in Thailand on a 45 day visa-exempt basis but need more time in the country (juggling commitments and plans at the moment). 

Is such an Extension from Immigration possible?

If so, how many days will be granted, and how much is the cost?

Thanks in advance.

You can get a 30 day extension for 1,900B. Go to the immigration office in Central Festival, it is less busy than the main airport immigration office.

You can apply for a 30 day extension of your visa exempt entry.