When I Googled Greist sewing, a Smithsonian site appeared on the list. On it, it states thtat Greist comany manufactured improved Singer sewing machines. Here is a link to a site that sells vintage and new machine attachments.
http://www.thesewbox.com/singer_low_...tachments.html and
http://www.thesewbox.com/f/How_to_De...Shank_Size.pdf This link points to determining shank size/type for purchasing attachments. There are only 4 types: slant, low, high, snap-on. So, it seems, that all low shank attachments fit all low shank machines. In my mind, though, you have to know your machine's needle position, too.