Venn Plot with More Than Four Sets"
In ggVennDiagram: A 'ggplot2' Implement of Venn Diagram

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(ggVennDiagram)
library(ggplot2)

Venn Diagram for more than four sets

With ggVennDiagram version less than 1.0, it only support 2-4 set Venn. By importing the polygon from venn , ggVennDiagram now supports 5-7 sets Venn.

genes <- paste0("gene",1:1000)
set.seed(20210507)
x <- list(A = sample(genes,100),
          B = sample(genes,150),
          C = sample(genes,200),
          D = sample(genes,250),
          E = sample(genes,300),
          F = sample(genes,350),
          G = sample(genes,400))

ggVennDiagram(x, label = "none", edge_size = 2) + scale_fill_distiller(palette = "RdBu")
ggVennDiagram(x[1:6], label = "none", edge_size = 2) + scale_fill_distiller(palette = "RdBu")
ggVennDiagram(x[1:5], label = "none", edge_size = 2) + scale_fill_distiller(palette = "RdBu")

Although ggVennDiagram supports 5-7 sets Venn diagram, I don't encourage to use them in scientific publications as it is difficult to separate the border of different sets in the plot (even with thick edges), especially for 7 and 6 sets Venn. Upset plot is a possible solution for these datasets. You may check a discussion of the Applications of Venn, Euler and Upset plot.