I have two hypergraphs which shares one vertex (HypergraphPlot function from Jaebum Jung's hypergraph plotting):

fig1 = HypergraphPlot[{{Subscript[d, 1], Subscript[d, 2]}, {Subscript[d, 1], Subscript[d, 3]}}, "SubsetBoundaryStyle" -> (Directive[EdgeForm[{Thickness[0.003], Black}], #] & /@ {Green, Red}), "SubsetBoundaryScale" -> {2, 2, 2, 2}, "SubsetEdge" -> False, PlotTheme -> "Classic"] 

So the plot figure is fig1 as the following:

I want to know how to show the overlap region and summing the color in the common regions such as fig2 (red + green ~ yellow)?

The stupid way I do is to draw one more additional hypergraph that only contains the common vertex and with the summed color -- this will show the region but in a manual way such as:

HypergraphPlot[{{Subscript[d, 1], Subscript[d, 2]}, {Subscript[d, 1], Subscript[d, 3]}, {Subscript[d, 1], Subscript[d, 1]}}, "SubsetBoundaryStyle" -> (Directive[EdgeForm[{Thickness[0.003], Black}], #] & /@ {Red, Green, Yellow}), "SubsetBoundaryScale" -> {2, 2, 2, 2}, "SubsetEdge" -> False, PlotTheme -> "Classic"] 

The manual way is not so nice due to the discontinued curves from different edges. Is there any clever way to do such things if the hypergraphs get more complicated? Thank you very much in advance! If something is unclear, thank you for pointing out!