You can, but I think to do so you basically have to reside in Thailand. You might be able to get an extension in Thailand on the 15 day - I do not know for sure. You might have to leave Thailand for a second visa run. Here's a link worth reading on travelfish:
#2 MADMAC has been a member since 6/6/2009. Posts: 6,957
"is there anyway I can get a 30 day visa"
1. Enter Thailand by air for a 30-day visa exemption - OR -
2. Get a proper tourist visa in Vientiane (60-day entry, extendable 30 more)
NB, a 15-day visa exemption by land can only be extended 7 days
Yes, the Thai consulate in Vientiane issues tourist visas (single or double entry). It takes 2 days, apply 8:30am then pickup next day 1pm (monday-friday only) and costs 1000 baht per entry. This gets you a 60-day entry and is extendable 30 days at immigration offices in Thailand for 1900 baht. Don't forget to bring 2 extra passport-size photos and photocopy of your passport photo page and Laos visa/entry page(s). Usually pretty busy there so allow time for standing around waiting.