Not base graphics, but ggplot
was made for this.
params = data.frame(alpha,beta)
gg <- do.call(rbind,lapply(1:nrow(params),function(i)
cbind(i,x,y=dbeta(x,params[i,]$alpha,params[i,]$beta))))
gg <- data.frame(gg)
library(ggplot2)
ggplot(gg,aes(x,y,color=factor(i))) +
geom_line(size=1)+
scale_color_manual("Alpha,Beta",
values=color,
labels=paste0("(",params$alpha,", ",params$beta,")"))+
theme(legend.position="bottom")
Note that with your definitions of alpha and beta, plots 4, 8, and 9 are identical, and plots 5 and 6 are identical.