Can I Convert My 30-Day Visa to a Longer Stay Visa While in Thailand?

I am a US citizen who was working and living in Indonesia until March 13th when the program I worked for urged everyone to terminate and return to the US. Last-minute changes by the Turkish govt (I was transitting through Istanbul) forbade the entry of animals to the country, so I had to leave my cat in Indonesia. As a result, I came to Thailand in hopes of being able to return and retrieve the cat in the near future and both of us return to the US. I arrived on a 30 visa on entry that I extended until May 18th before the Thai government extended visas to 4/30. Is there a way to convert this visitor visa into a longer stay visa now that I am already in Thailand? I won't be able to return to Indonesia by May 18th and I don't want to have to return to the US without the cat.