Supercoiling is the large-scale secondary coiling or buckling of a structure that is already coiled at a smaller scale. Here, we show experimentally that a fluidmechanical analog of supercoiling can occur when a thin "rope" of viscous fluid falls vertically from a great height onto a surface. For appropriate values of the viscosity ν, the flow rate Q, and the fall height H, a primary coiling instability of the rope forms a hollow coiled cylinder that then experiences a secondary buckling instability in the form of periodic folding accompanied by slow rotation of the folding plane. To delineate the conditions under which this supercoiling state appears, we carry out systematic laboratory experiments over wide ranges of Q and H using several fluids with different viscosities. We find that five different states of the rope are possible: supercoiling (SC), periodic collapse of the fluid cylinder formed by a primary coiling instability (PC), periodic folding (F), and steady coiling (C) of the rope itself, and axisymmetric stagnation flow(S). Up to three of these states can be realized for a given set of experimental conditions, and we determine detailed state diagrams showing which combinations are observed as a function of ν, Q, and H. The selection of the states is controlled by the dimensionless parameter gHQ2/ν4 (g is the gravitational acceleration), which is directly related to the ratio of the rope radius a to the coil radius R in steady primary coiling with the parameters ν, Q, and H.