Recursively plotting specific elements in a list of lists


I am trying to build band structures and am looking to generate a general code that will work regardless of my list size. Here is what I am trying to do: say I have a list like

list = {{0.0, 1, 2, 3}, {0.1, 4, 5, 6}, {0.2, 7, 8, 9}, {0.3, 10, 11, 12}}; 

and I want to plot the nth element of each list against the first element of each list. How can I tell Mathematica to automatically produce a set of lists to plot like shown below

k = {0.0, 0.1, 0.2, 0.3}; band1 = {1, 4, 7, 10}; band2 = {2, 5, 8, 11}; band3 = {3, 6, 9, 12}; Show[ListLinePlot[k, band1], ListLinePlot[k, band2], ListLinePlot[k, band3]] 

Doing it manually one band at a time is possible but a waste of time when I have n=36+ bands. Any help would be much appreciated!