Draw a "grid" between arranged plots

grid.polygon() is quite manual but I think it can do the trick:

Using RStudio

library("ggpubr")
library(ggplot2)
library(gridExtra)
library(grid)
p1 <- ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + ggtitle("Plot 1")
p2 <- ggplot(iris, aes(x = Petal.Length, y = Petal.Width)) + geom_point() + ggtitle("Plot 2")
p3 <- ggplot(iris, aes(x = Sepal.Length, y = Petal.Width)) + geom_point() + ggtitle("Plot 3")
p4 <- ggplot(iris, aes(x = Petal.Length, y = Sepal.Width)) + geom_point() + ggtitle("Plot 4") +
  facet_wrap(~Species)

plot.list <- list(p1, p2, p3, p4)

ggarrange(plotlist = plot.list)
x = c(0, 0.5, 1, 0.5, 0.5, 0.5)
y = c(0.5, 0.5, 0.5,0, 0.5, 1)
id = c(1,1,1,2,2,2)
grid.polygon(x,y,id)

Using Shiny (Edit)

When doing it within a shiny-app, ones needs to add the grid using annotation_custom(), as follows:

    ggarrange(plotlist = plot.list) + 
    annotation_custom(
             grid.polygon(c(0, 0.5, 1, 0.5, 0.5, 0.5),
                          c(0.5, 0.5, 0.5,0, 0.5, 1), 
                          id = c(1,1,1,2,2,2), 
                          gp = gpar(lwd = 1.5)))

Not sure if this will work for you, but you can just put borders around your individual plots. However, this includes borders on the outside of the layout. Your description seems like you're not opposed to that, but there are only inner gridlines in your example plot.

You could add the theme call when you create the plots; rather than editing the plot creation, I just did it to each plot in the list before sticking them all together.

library(ggpubr)
library(ggplot2)

#### same plot creation here ######

plot.list <- lapply(list(p1, p2, p3, p4), 
                    function(p) p + theme(plot.background = element_rect(color = "black")))

ggarrange(plotlist = plot.list)