Styling overlapping polygons of different layers

I use the 'Line Pattern Fill' with a different colour and line fill rotation for each layer.

It can be useful to create a variable in the project properties to use as the spacing between lines, fill line weight etc, this will make it easier to adjust all layers by changing one or two variables instead of lots of variables for different layers.

See below for examples:

Single Layer

Two Layers

Three Layers

You can set each layer to render differently when there is an overlap with another layer. Go to the style, expand layer rendering, then select multiply under layer blending mode.

If you want to see overlaps with polygons from the same layer, you could (also) set the feature blending mode to multiply.

As another option, you may be able to add a layer dedicated to show the overlapping area, so that you can keep original three polygon layers, showing thin outlines only.

Run Build virtual vector tool (in QGIS Processing Toolbox > Vector general), with Create Unioned VRT option.

Put the newly created layer underneath and set color and transparency.