Matplotlib duplicate subplot in multiple figures without redrawing for each figure

I am creating about one dozen figures with subplots. There is one subplot that is the same for all the figures. However, it takes a loonnggg time to draw. Is there a way to only draw this subplot once and then replicate it in each figure? (Not the same thing as this accepted answer, which just defines a function that redraws the subplot every time.)

A snippet of the large source data file for the slow-drawing plot is below, as well as my current code for generating the subplot.

Code:

fig1 = plt.figure()
ax1 = plt.subplot2grid((2,2), (0,0), rowspan=2, colspan=1)
for ii in df_lines.Line_ID: ## df_lines.Line_ID = max(df_points.ID)
    temp = df_points.loc[df_points.ID == ii]
    df_myline = temp.sort_values(by='Order_ID', ascending=True)
    del temp
    x = df_line.X
    y = df_line.Y
    ax1.plot(x, y)

df_points Snippet: Note there are decimals here in X,Y they just got cut off here

ID  Order_ID    X   Y
1   1   -116    35
1   2   -116    35
2   1   -116    35
2   2   -116    35
3   1   -116    35
3   2   -116    35
3   3   -116    35
4   1   -116    35
4   2   -116    35
5   1   -116    35
5   2   -116    35
6   1   -116    35
6   2   -116    35
7   1   -116    35
7   2   -116    35
8   1   -116    35
8   2   -116    35
9   1   -116    35
9   2   -116    35
10  1   -116    35
10  2   -116    35
10  3   -116    35
10  4   -116    35
10  5   -116    35