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Context

More often than not I end up doing plots one after the other so that I have a set of plots with the same colour style.

When I want to make it more publishable ready, I would like to reassign colours to each line.

How to assign colours from a given style to existing sets of plots?

Example

pl1= Plot[Sin[x],x,0,4Pi];
pl2= Plot[Cos[2x],x,0,4Pi];
Show[pl1,pl2];

Attempt

I while back I wrote the following function

Clear[ShowColor];
ShowColor[list___]:=ShowColor[list]/; Length[list]>1;
ShowColor[list_,ColorRange->color__,opt___]:= Module[len=Length[list],
 Table[list[[i]] /. RGBColor[_,_,_]->
 GradientColor[color][(i-1)/(len-1)],i,len]//Show[#,opt]&]
ShowColor[list_,opt___]:= Module[len=Length[list],
 Table[list[[i]] /. RGBColor[_,_,_]->
 GradientColor[ColorData[10] /@ Range[10]][(i-1)/(len-1)],i,len]//Show[#,opt]&]

which uses the GradientColor Package,
so that

ShowColor[pl1,pl2]

produces

But I am left with the impression that it could be done more elegantly and generally with the modern version of Mathematica, making use of the set of default styles
and working in harmony with other features.

Also, my implementation is not very robust. For instance,

 Show[pl1, pl2] // ShowColor 

fails.

What would be great would be to have a function which
e.g. would take standard Options such as

 ShowColor[plots,PlotStyle-> ColorData[10]]

or

 ShowColor[plots,PlotStyle-> Directive[Dashed,Blue]]

Any suggestion on how to make this as generic as possible?

Thanks!

A simple way is to pass the coordinates in the plots to ListLinePlot.

recolor[plot_, opts___] := ListLinePlot[
 Cases[plot, Line[coords_] :> coords, Infinity],
 opts
 ]

Show[
 recolor[pl1, PlotStyle -> Directive[Blue, Dashed]],
 recolor[pl2, PlotStyle -> Red]
 ]

It can also be used to recolor already combined plots:

recolor[
 Plot[Sin[x], Cos[2 x], x, 0, 4 Pi],
 PlotStyle -> 
 Directive[Blue, Dashed],
 Red
 ]

And it also works on this:

recolor[Show[pl1, pl2],
 PlotStyle -> 
 Directive[Blue, Dashed],
 Red
 ]

Using DLichti's ingenious idea / function from this q/a:

dLichtiIncrement[n0_Integer: 0, n1_Integer: 0, f_Function: Identity] := 
 Module[N0 = n0, N1 = n1, (If[# <= N1, N0 = N0 + N1]; N1 = #; f[N0 + #]) & ]

to define a function color which increments the color every time it is invoked as color[1]:

ClearAll[color, reColor]
color = dLichtiIncrement[(ColorData[97][#] &)];
reColor[] = # /. _?ColorQ :> color[1] &;
reColor[_] := Module[, ClearAll[color]; 
 color = dLichtiIncrement[(ColorData[97][#] &)]; reColor[]]

Examples:

pl1 = Plot[Sin[x], x, 0, 4 Pi];
pl2 = Plot[Cos[2 x], x, 0, 4 Pi];
Show[pl1, pl2]//reColor[]

ContourPlot[Cos[x] + Cos[y], x, 0, 4Pi, y, 0, 4Pi] // reColor[]

Plot[x Sin[x], x Cos[x], Sin[x Cos[x]], x, 0, 2 Pi, 
 PlotTheme -> "Monochrome", Filling -> Axis, FillingStyle -> Opacity[.5]] // reColor[]

ContourPlot[Evaluate[Sum[Sin[RandomReal[5, 2].x, y], 5]], x, 0, 5, y, 0, 5,
 PlotTheme -> "Monochrome"] // reColor[]

 ContourPlot[Cos[x] + Cos[y], x, 0, 4 Pi, y, 0, 4 Pi,
 ContourShading -> False] // reColor[]

You can also use color[1] in setting ChartStyle/PlotStyle:

BarChart[1, 2, 3, 1, 3, 2, ChartStyle -> Table[color[1], 3]]

Using reColor[blah] @ Red resets color[1] to its initial state:

 reColor[blah] @ Red == ColorData[97][1]

True