So nat'ralists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller fleas to bite 'em.
And so proceeds ad infinitum.
-Jonathan Swift
What you're thinking of is called hyperparasitism, and it's absolutely a thing that exists, although perhaps not to the degree that you're planning for your story. From an evolutionary perspective it's a bit odd that all species would choose parasitism over mutualism or predation, but just because it's unlikely doesn't mean it's impossible.