I would not be surprised if there are designs that look like cross stitch out there. I even thought that I had one in my collection of designs for my embroidery machines. I suggest you go on a site that sells machine embroidery designs and search it. I know that I have designs for red work and lace designs. While I have a large number of design cards etc. I am not crazy about constantly having to change threads so I tend to use multicolored threads and just keep sewing with them instead of changing every time the pattern expects me to. The results are quite nice especially if the design is fairly simple.