I found this model which looked really cool but didn't have a good base. I remade it from scratch in Fusion 360 (F3D file included) to include a base and also have smaller holes sized for monofilament fishing line.

Assembly involves getting knots above and below each of the pieces. You can see this in the video for the original model. You have to get a good amount of tension in each segment. Squeeze the arms together when knotting above each part to ensure tension in the segment between the arms as it springs back open.

I found that 3 pieces is about as high as I can get it with my level of skill but if you can get enough tension in the segments you might be able to go even higher.

Assembly is difficult right now but I think it can be simplified by replacing the holes with a slot that a pre-knotted string is slid into. Will revise this model eventually to make that change.