Yes the die cutters can. Cricut has some pretty cartridges with these kind of designs. I own a couple of them. I can't think off the top of my head what the cartridges are. Maybe somebody will save me, lol. I am tired.
I want to say the Paper Lace cartridges. If you can log into CCR you can browse the images.
The Cameo will cut those designs with better accuracy and detail. I think this is where Cameo's store outshines the other cutters is their inventory of quatrefoil designs. I am not trying to sell you on the Cameo. If I was reading your post correctly you mentioned cutters. I threw it out just in case you were looking.
Hope that helps.