All the methods below add three styled curves, _**"while all other curves stay in the default style."**_

### ContourPlot


**1.** You can use the options `MeshFunctions` and `Mesh` to add additional contours:

    ContourPlot[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
     PlotPoints -> {30, 30}, PlotRange -> {{-10, 10}, {-10, 10}}, 
     ColorFunction -> "Rainbow", ImageSize -> 500,
     MeshFunctions -> {Sin[# - #2] + Cos[# + #2] &}, 
     Mesh -> {Thread[{{0., -1., 1.}, 
         Thread[Directive[{Green, Red, Blue}, Thick, Opacity[1]]]}]}]

[![enter image description here][1]][1]

**2.** Generate the list of contours using [`FindDivisions`](https://reference.wolfram.com/language/ref/FindDivisions.html) and style each contour as you like:

    automaticcontours = FindDivisions[{-2, 2}, 10];

    styledcontours = {{-1, Directive[Thick, Red]}, 
       {0, Directive[Thick, Green]}, {1, Directive[Thick, Blue]}};

    contours = DeleteDuplicatesBy[First]@
       Join[styledcontours, Thread[{automaticcontours, Automatic}]];

    ContourPlot[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
     PlotPoints -> {30, 30}, PlotRange -> {{-10, 10}, {-10, 10}}, 
     ColorFunction -> "Rainbow", ImageSize -> 500, 
     Contours -> contours]

[![enter image description here][2]][2]

**3.** Post-process `ContourPlot` output to restyle selected contours:

    cp = ContourPlot[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
      PlotPoints -> {30, 30}, PlotRange -> {{-10, 10}, {-10, 10}}, 
      ColorFunction -> "Rainbow", ImageSize -> 500];

    Replace[cp, {Tooltip[{d___, l__Line}, t : (0. | 1. | -1.)] :> {Thick, Opacity[1], 
        t /. {0. -> Green, -1. -> Red, 1. -> Blue, _ -> {d}},  Tooltip[{l}, t]}}, All]

[![enter image description here][3]][3]

**4.** Yet another method is to extract the contours from `cp` and redo `ContourPlot` using styled contours:

    automaticcontours = Cases[cp, Tooltip[_, t_] :> t, All]
>     {1.5, 1., 0.5, 0., -0.5, -1., -1.5};

    styledcontours = Thread[{{0., -1., 1.}, 
         Thread[Directive[{Green, Red, Blue}, Thick, Opacity[1]]]}];

    contours = Join[styledcontours , Complement[automaticcontours, {0., -1., 1.}]];
    
    ContourPlot[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
     PlotPoints -> {30, 30}, PlotRange -> {{-10, 10}, {-10, 10}}, 
     ColorFunction -> "Rainbow", ImageSize -> 500, 
     Contours -> contours]

[![enter image description here][4]][4]

### Plot3D

**1.** Use [`FindDivisions`](https://reference.wolfram.com/language/ref/FindDivisions.html) to generate a  mesh list (that matches the automatically generated one) and add your list of styled mesh lines and use the combined list as the setting for `Mesh`:

    automaticmeshlines = Most @ Rest @ FindDivisions[{-2, 2}, 18];

    styledmeshlines = {{-1, Directive[Thick, Red]}, {0, 
        Directive[Thick, Green]}, {1, Directive[Thick, Blue]}};

    mesh = DeleteDuplicatesBy[First]@
      Join[styledmeshlines, Thread[{automaticmeshlines , Automatic}]];

    Plot3D[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
     PlotPoints -> {30, 30}, PlotRange -> {{-10, 10}, {-10, 10}, {-3, 3}},
     ColorFunction -> "Rainbow", ImageSize -> 500, 
     Method -> {"RotationControl" -> "Globe"}, SphericalRegion -> True,
     MeshFunctions -> {#3 &},
     Mesh -> {mesh}]

[![enter image description here][5]][5]

**2.** Add constant functions in the first argument of `Plot3D` corresponding to the desired levels, set their `PlotStyle` to `Opacity[0]` and use the option [`BoundaryStyle`](https://reference.wolfram.com/language/ref/BoundaryStyle.html) to set the directives for the intersection of the main surface with the added planes:

    Plot3D[{ 0., -1., 1., Sin[x - y] + Cos[x + y]}, {x, -10, 10}, {y, -10,
       10}, PlotPoints -> {30, 30}, 
     PlotRange -> {{-10, 10}, {-10, 10}, {-3, 3}}, 
     MeshFunctions -> (#3 &), 
     PlotStyle -> {Opacity[0], Opacity[0], Opacity[0], Automatic}, 
     ColorFunction -> "Rainbow", ImageSize -> 500, 
     BoundaryStyle -> {1 -> None, 2 -> None, 3 -> None, 
       {4, 1} -> Directive[Green, AbsoluteThickness[4], Opacity[1]], 
       {4, 2} -> Directive[Red, AbsoluteThickness[4], Opacity[1]],
       {4, 3} -> Directive[Blue, AbsoluteThickness[4], Opacity[1]]}, 
     Method -> {"RotationControl" -> "Globe"}, SphericalRegion -> True]

[![enter image description here][6]][6]


**3.** Post-process to restyle selected mesh lines:

    p3d = Plot3D[Sin[x - y] + Cos[x + y], {x, -10, 10}, {y, -10, 10}, 
      PlotPoints -> {30, 30}, 
      PlotRange -> {{-10, 10}, {-10, 10}, {-3, 3}}, 
      MeshFunctions -> (#3 &), ColorFunction -> "Rainbow", 
      ImageSize -> 500, Method -> {"RotationControl" -> "Globe"}, 
      SphericalRegion -> True];
    
    Normal[p3d] /. Line[x_, ___] :> 
      {Round[x[[1, -1]], 0.1] /. Append[Thread[{0., -1., 1.} -> 
        Thread[Directive[{Green, Red, Blue}, Thick, Opacity[1]]]], _ -> {}],  Line[x]}

[![enter image description here][7]][7]


  [1]: https://i.sstatic.net/RVr19.png
  [2]: https://i.sstatic.net/tQpg3.png
  [3]: https://i.sstatic.net/wlK9k.png
  [4]: https://i.sstatic.net/ywDp1.png
  [5]: https://i.sstatic.net/zCiLI.png
  [6]: https://i.sstatic.net/amvyb.png
  [7]: https://i.sstatic.net/81JbZ.png