How can I reduce the width of each individual boxplot in Base R?
I do not want to change the relative sizes of the boxplots, which I understand can be done with the width argument
(this is not the same question as this post, which asks about removing whitespace)
boxplot(mpg ~ cyl,
data=mtcars)

You can set the default width using the boxwex= parameter. More information on these parameters are actually found in the ?bxp help page which does the boxplot drawing. There's a mention of this when describing the ... parameter in the ?boxplot help page.
boxplot(mpg ~ cyl, data=mtcars, boxwex=.2)

The graphic parameter you want is boxwex, see help("bxp"), the function that does the plotting part of the box-and-whiskers plot.
old_par <- par(mfrow = c(3, 1))
boxplot(mpg ~ cyl, data=mtcars, boxwex = 0.1)
boxplot(mpg ~ cyl, data=mtcars, boxwex = 0.4)
boxplot(mpg ~ cyl, data=mtcars, boxwex = 0.8)
par(old_par)

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