Dependency would form the bases for the extension of an "O" visa.  If you have a Thai child or children you may stay in Thailand based on dependancy. You would apply for an "O" visa based on having a minor child in Thailand. There are certain regulations governing this stay. You would apply for an "O" visa a Thai embassy abroad which is valid for 90 days and extend it in country thereafter.

TheThai "B" or Business Visa can be extended to a one year visa in country as follows. The extension of the visa is normally based on employment and as such there are certain regulations governing the company who is employing you. These can be set down as follows:

This is one of the most common forms of Thai Visas issued by the Thai embassies worldwide. Most Thai Tourist Visas are either single entry, 60 days or double entry - valid for 120 days based over two legs. 

There are different Thai visas and each Thai visa has it own procedure to extend its validity,  This is a very brief overview of what is needed to have each one extended and whatthe documents that you will be required to have.