Yes, the AE-1 can do multiple exposures but not easily. You have to rewind the film and wind again since there is no way to cock the shutter without winding and there is no dedicated multiple exposure feature. You need to rewind and look at the little dot on the rewind button to get the spacing right. Not easy to do but it is what he has so you have to work with what you've got.
Originally Posted by Christopher Walrath
You could 'black hat' it though, put it on a tripod and cover the lens with a 'hat' and take it off for seconds at a time during totality, replacing the 'hat' each time. At the darkest point of totality it may take 30s for the exposure which will be blurred but that's what you get unless you have a driven mount.