Varied PlotRange for plots combined using Show

Question

I would like to create a so called Stacked Plot type of view to display a combination of data. Perhaps there already is a built in function in Mathematica, but I didn't manage to find it. So, I decided to simply shift the X and Y axis values of plots by a certain value and combine them using Show.
Here is the example code how I tried to do it:
Do[
 Subscript[data, i] = Table[{x, Sin[x + i] + 2*i}, {x, 0, 10, 0.1}];
 Subscript[lpl, i] = ListLinePlot[Subscript[data, i], PlotRange -> {{0 + 0.1*i, 10 - 0.1*(10 - i)}, {-1.2, 22.2}}]
, {i, 0, 10}];
Show[Table[Subscript[lpl, i], {i, 0, 10}], Axes -> None, Frame -> {{None, None}, {True, None}}, PlotRange -> {{-0.1, 10.1}, {-1.2, 22.2}}]

You can see, that I shifted the x values of PlotRange of each consequent plot by a certain value. However, in the output all of the plots seem to have the same PlotRange values. The resultant output looks pretty rectangular, like this:

Here are the questions:

Is it possible to combine several ListLinePlots having different PlotRange values using Show so, that they retain their individual PlotRanges, i.e. will be clipped in a combined plot?
Perhaps there is another, better solution to make a Stacked Plot? Here is an example of how a Stacked plot I am aiming for looks like:

Bob Hanlon · Accepted Answer

data = Table[{x, i, Sin[x + i]}, {i, 0, 10}, {x, 0, 10, 0.1}];

ListPointPlot3D[Evaluate@data]

Graphics3D[{AbsoluteThickness[3.25],
  Transpose[{
    Table[ColorData[97][n], {n, Length[data]}],
    Line /@ data}]},
 BoxRatios -> {1, 1, 1/2},
 Axes -> True]

Nasser · Answer

If I understand you right (if not, please let me know, and will delete this), you want to combine the plots but each have it own plot range.

I would not use Show. Just use ListLinePlot. Show takes information from the first graphic object it is given.  So I would simply do

Do[data[i]=Table[{x,Sin[x+i]+2 i},{x,0+0.1 i,10-0.1 (10-i)}],{i,0,10}];
ListLinePlot[data[#]&/@Range[0,10]]

ps. I changed your subscripts with indexed, as it is easier to type for me.

kglr · Answer

You can use TemporalData to construct your input data and then use TimeSeriesRescale on individual time series to get a perspective look/feel:
numberofseries = 20;

tds = Table[TemporalData[Table[Sin[x + i] + 2*i, {x, 0, 10, 0.1}], {0, 10}],
   {i, numberofseries}];

ClearAll[xaxis]
xaxis[a_, b_] := {GrayLevel[.4], Thickness -> Absolute[0.2], 
     {Line[#[[{1, -1}]]], Line[{#, Offset[{0, -5}, #]}] & /@ #, 
      Text[#[[1]], Offset[{0, -15}, #]] & /@ #} & @ Thread[{Range[a, b], 0}]};

ListLinePlot[tds, ImageSize -> Large, Axes -> False, 
 Epilog -> xaxis[0, 10], AspectRatio -> 1/2, ImagePadding -> 20, 
 PlotRangeClipping -> False, Ticks -> {Range[0, 10], All}]

ClearAll[rescaleTD]
rescaleTD[ls_: .1, rs_: .1] := MapIndexed[TimeSeriesRescale[#, 
   Flatten[# /@ {"FirstTimes", "LastTimes"}] + {ls, rs} #2[[1]]] &, #] &;

Grid @ Transpose @ 
    (ListLinePlot[#, ImageSize -> 360, Axes -> False, 
        Epilog -> xaxis[0, 10], AspectRatio -> 1/2, 
        ImagePadding -> {{5, 5}, {20, 5}}, 
        PlotRangeClipping -> False, Ticks -> {Range[0, 10], All}] & /@
     Through[{rescaleTD[#, #], rescaleTD[#, -#], rescaleTD[#, -#/2]} @ tds] & /@ 
     {.1, .15, .2})

Varied PlotRange for plots combined using Show

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