Yes. Each row in the CSV makes 1 composite. So you would make additional rows for each memory mate. So it you had 3 memory mates, you would have 3 rows for every image file in column A. Then use the TEMPLATEFILE header to assign the PSD for each row.
Also, just FYI….
It process in the order of the columns in the CSV. So it will run fastest if you sort the CSV by the TEMPLATEFILE column when it is ready instead of by column A. That way it won’t need to close and open the PSD template for every image. It would then keep the template open to run all images for that template before closing the template and opening the next to run all images through the next template. This can be a huge time saver if using a larger template as that could add several seconds to every image if closing and opening 3 time for every source image.