What are the requirements for renewing a Non-O visa and applying for a multiple entry permit in Thailand?

It depends on what you are renewing, if it's a retirement visa then check out the Pattaya expat club website for guides.

You can all forms at Immigration

I went yesterday. First time.

TM7 for application of temporary stay.

TM8 for application for reentry permit.

Although because I went in the afternoon, by the time I got my TM7 processed the officer told me the desk for reentry permit was closed.

the application for the next 1-year extension and the application to the re-entry permit are two totally separate applications. First you need the 1-year extension of the temporary stay permit approved, and only after that you can buy a re-entry permit for your 1-year extended stay permit, either single for 1000 Baht, or if you wish to exit more often than three times during this one-year stay permit, a multi re-entry permit for 3800 Baht

I apply at the same time. Different forms but my local immigration issues them at the same time

Do you mean to apply for a multiple re-entry permit? Get your extension first then apply for it?

Two different things. First is the extension. Once you get your extension, you get a single or multi re-entry permit. And no, the forms are different. Go to their website, they should have a list of what you need to submit as well as forms you can download and print. Fill out in blue ink and everything including the copies of your one year lease, landlord ID card, chanote title, your passport ID page and entry and extension stamps, a hand drawn map of where you live, a video tour of your house, a photo in front of your house number. At least that is what is required in Phuket. Oh and your bank statement for the year and bank letter. The ฿800K has to be in your account for two months before you can apply. I had to do everything in duplicate.