Thank you for the welcome and for the input!
I found out… it is a width and patience problem.
Believe it or not, I got stubborn today and decided to risk it and buy a Cuttlebug embossing folder. (I thought if it did not work out, I could always try to sell it on the well-known online marketplace).
I have Double Do plates and I have Cuttlebug plate “b”. I tried out the different plates to see what happens. Anyway, the results are fantastic. It does work and you have to combine a “b” Cuttlebug plate with the grey Double-Do plate to get the best results. I was so excited. The Cuttlebug Folders are flexible, which also appealed to me.
I also bought a cutting template from Cuttlebug. It did not work out with the Double-Do as it was too thick, but I think it is a matter of finding a plate with the proper width.
I also have a few Fiskars Texture Plates. I got curious. They also work with the Double-Do but could crack at the top (where the holes are to add to the Shape-Boss) so I would not suggest it, really. They are not really flexible like the Cuttlebug Folders. But once cracked, and taped together, the Texture Plates worked fine. It was as if the crack took the “pressure” off of the plate.