Increase PDF margins by reducing size of content (without changing overall page size)

You can also use Ghostscript for that.

1. Increase page media size, keep page content size

Assuming your page size is A4 (that is 595x842 points), and you want to add a margin of 1 additional inch (72 points) on each edge: that gives you a new page size of 739x986 points.

Then the Ghostscript command is this:

gs -o out1.pdf                                       \
   -sDEVICE=pdfwrite                                 \
   -g7390x9860                                       \
   -c "<</Install {72 72 translate}>> setpagedevice" \
   -f input.pdf

The 72 72 translate part is required to move the image by 1 inch to the left and 1 inch up. Otherwise the page image would appear in the lower-left corner of the new, bigger page.

2. Keep page media size, shrink page content size

Assuming your page size is A4 (that is 595x842 points), and you want to shrink the original content (and center it on the page) by such a percentage that an additional margin of 1 additional inch (72 points) is added to each edge: that gives you the new page content dimensions of 451x698 points. (At the same time this is not a "keep-aspect-ratio" shrink, otherwise you'd create different gutter for bottom/top and left/right!)

This means scaling in horizontal direction as 451/595 == 75.79% and in vertical direction as 698/842 == 82.89%.

Also, if you would not again the 72 72 translate operation, the shrinked page content would appear on the lower left corner:

gs -o out2.pdf                                         \
   -sDEVICE=pdfwrite                                   \
   -g5950x8420                                         \
   -c "<</Install {.7579 .8289 scale
                   72  72  translate}>> setpagedevice" \
   -f input.pdf

Is there a way to resize the content so there is more whitespace, without changing the overall size of the page?

You can use File > Print > Custom Scale and choose an appropriate scale factor.