Can I extend a 60-day tourist visa in Thailand and convert it to a business visa?

About how much it cost for an extension  visa

You can usually convert from tourist to non-B visa inside of Thailand if your company will support it and the immigration office allows it. You would need to check with the company as doing a conversion takes A LOT of paperwork, so much that many companies cannot or will not provide it and send their employees to a Thai embassy in a neighboring country to get the visa.

So you'll need to check with your company to see if they'll support it and check with the immigration office that will be used to see if they will allow it.