There are examples like наддать пару and поддать пару (not my favorite Russian words, but still they both exist).
They have the same meaning, at least that is what gramota.ru suggests: наддать, meaning 1 and поддать, meaning 3.
At the same time, prefixes над- and под- have exactly opposite meanings, at least as long as they refer to the position in space (над- stands for above, под- stands for under).
How come that adding prefixes with opposite meaning to the same stem results in the words with the same meaning?
поднажать
featuring bothна-
(though notнад-
) andпод-
prefixes.