You can use `Show` to combine graphics of the same type:

    g1 = Plot3D[x^2 - y^2, {x, -3, 3}, {y, -3, 3}, 
      RegionFunction -> Function[{x, y, z}, 2 < x^2 + y^2 < 9]];
    
    g2 = SphericalPlot3D[
      1 + Sin[5 θ] Sin[5 φ]/5, {θ, 0, π}, {φ, 0, 2 π}, 
      Mesh -> None, RegionFunction -> (#6 > 0.95 &), PlotStyle -> FaceForm[Orange, Yellow]];
    
    Show[g1, g2]

![Mathematica graphics](https://i.sstatic.net/46ovm.png)


----------

Here is one way that you might construct a compound graphic:

    funcs = {x^2 - y^2, Sin[x]^2 + 2 Cos[y]^2};
    
    regions = {Function[{x, y, z}, 1 < x^2 + y^2 < 5], 
               Function[{x, y, z}, 2 < x^2 + y^2 < 9]};
    
    styles = {Red, Green};
    
    MapThread[
      Plot3D[#, {x, -3, 3}, {y, -3, 3}, RegionFunction -> #2, PlotStyle -> #3] &,
      {funcs, regions, styles}
    ] // Show

![Mathematica graphics](https://i.sstatic.net/aNPKv.png)

----------

You may also find utility in `Piecewise`:

    pw = Piecewise[{
           {2 Sqrt[x],   0 <= x <= 1  },
           {4 - 2 x  ,   1 <  x <  2.5},
           {2 x - 7  , 2.5 <= x <= 4  }
          }, Indeterminate]
    
    Plot[pw, {x, -1, 5}]

![Mathematica graphics](https://i.sstatic.net/KdmmS.png)