Thanks @ben-frederickson for both the answer and your fine venn.js library. If the user would like to solve the problem in R with the new d3vennR htmlwidget, here is my answer. It is not the most efficient method, but it works.

# devtools::install_github("timelyportfolio/d3vennR")

library(d3vennR)
library(sets)

sets_df <- read.csv(
  textConnection("Ath,Fve,Mdm,Pcmm,Pper,Pmum,Counts
1,0,0,0,0,0,901
0,1,0,0,0,0,14764
0,0,1,0,0,0,19408
0,0,0,1,0,0,17714
0,0,0,0,1,0,16849
0,0,0,0,0,1,17572
1,1,0,0,0,0,823
1,0,1,0,0,0,846"
  )
)

# get all sets provided and their counts/size
sets_list <- apply(
  sets_df
  ,MARGIN=1
  ,function(rw){
    list(
      sets = as.list(colnames(sets_df)[which(rw==1)])
      , size = as.numeric(tail(rw,1))
    )
  }
)

# get all set combinations to fill with size = 0 where missing
sets_combinations <- lapply(
  # answer by venn.js authors only goes to combinations of m=2
  #  this goes to combinations of m = sets - 1
  seq.int(1,length(colnames(sets_df))-2)
  ,function(m){
    t(combn(colnames(sets_df)[-length(colnames(sets_df))],m=m))
  }
)

# now combine the sets and sizes provided in data with the sets and 0 
sets_venn <- unlist(
  lapply(
    sets_combinations
    ,function(x){
      apply(
        x
        ,MARGIN=1
        ,function(y){
          # this gets sets of 0 which are not in the data provided
          if(!set_contains_element(
            as.set(lapply(sets_list,function(z){as.set(unlist(z$sets))}))
            ,as.set(y)
          )){
            list(sets=y,size=0)
          } else {
          # this gets sets with their sizes given by the partial data provided
            unlist(
              Filter(
                function(z){
                  set_is_equal(as.set(y),as.set(unlist(z$sets)))
                }
                ,sets_list
              )
              ,recursive=F
            )
          }
        }
      )
    }
  )
  ,recursive=F
)


# produce the Venn Diagram in R with the transformed data
d3vennR( data = sets_venn )

The venn package can handle up to 6 rings, see https://pypi.org/project/venn/

One way may use the package eulerr. However, your question isn't very clear so I let you play with the package

See the example below :

library(eulerr)

fit <- euler(c("A" = 10, "B" = 10, "A&B" = 8, "A&B&C"=3))

plot(fit,
     fills = list(fill = c("red", "steelblue4","green"), alpha = 0.5),
     labels = list(col = "black", font = 4),quantities = T)