Do I need a reentry stamp with a multiple entry O-A visa in Thailand?

No

The OA is valid for a year, and on each entry you get stamped in for one year ( if you have insurance for that time). If you enter just before that year is up you get stamped in for a year - but your visa has now expired (or will soon). Your entry stamp is good for a year so to keep that alive you’d need a reentry permit (single or multiple-up to you).

So simple answer for the first year you don’t need a permit, but for the second year you would.