ggplot text elements (not sure about the label aesthetic) accept expressions. Check out ?plotmath to see what's possible. For sub-subtitles:
library(ggplot2)
ggplot() +
labs(
title = "Title size",
# Plotmath works on expressions
subtitle = expression(
# Plotmath expressions can't use "\n", so this vertically arranges
atop(
"Subtitle size",
atop(
# Small font
scriptstyle("Small"),
# Tiny font
scriptscriptstyle("Tiny")
)
)
)
)

Notice how the lines are made to follow the same center. I'm not sure if that can be changed. Also, I don't know if it's possible to set each subtitle line's font size independently.