How to manipulate a Dataframe which contains multiple lines of signals and plot signal vs. time using parallel_coordinates?

Question

I work with a quite large table (50MB) which has a similar format to the following table:

I would like to manipulate the dataframe using pandas' stack, unstack, set_index, pivot, pivot_table function or in any other idiomatic fashion, so I'll be able to plot all size signals as function of time. For example, plotting the size column at the different time points using parallel_coordinates.

iteration   weight  count edge  blobs   days    frame   start   time    size
1   7   600 100 1000    0   0   0   0
1   7   600 100 1000    1   2   2   13.5
2   3   600 100 333 0   0   0   19.5
2   3   600 100 333 1   2   2   25.5
3   4   600 100 1000    0   0   0   22.5
3   4   600 100 1000    1   2   2   24

Then once I plot the individual signal as function of time, I want to average over the different iterations of the same physical condition (where weight, count, edge, blobs, days time are the same).

EDIT:

I think that if I find an easy way to convert the original dataframe to this one, we will be able to plot all the size vs. time signals:

Or maybe something like that: