Πολύς-πολλή-πολύ become περισσότερος-περισσότερη-περισσότερο in comparative and πλείστος-πλείστη-πλείστο in the absolute superlative. So the base adjective is πολύς.
A thought of mine: In ancient greek, the comparative form of πολύς was πλείων which is no longer used and relates to πλεόνασμα, πλέον, επιπλέον etc. Περισσότερος actually seems to be the "normal and regular" comparative form of περισσός=excessive. At some point in history, there must have been an overlap between the two and they got fused this way, the same way the φαγ- stem got into the τρώ(γ)ω verb or the είπ- stem got into the λέγω verb etc (with the difference that περισσός stayed a word on its own with a different meaning).
Maybe it has περίσσιος? It's another form of it. Also περισσός is the Attic form of περιττός (and that's why περισσεύω can also mean "to be superfluous") in Ancient Greek (I think that you have said that you have studied ancient greek?-that's why I add all that info) but they got to take on different meanings with περιττός being "superfluous, redundant" and περισσός being "excessive".
I had ancient greek years ago while studying linguistics, but I quit after the first semester. I couldn't take all those irregular verbs. Mostly I know Germanic languages, and there is only a small group of irregulars. But I also studied Sanskrit, Lithuanian, Russian.. (and Finnish and Eskimo) to get a feel for language history and types.
According to "tips" this adjective is the superlative for μεγαλος so the translation should be "the biggest" not "the maximum". Mind you, this was a "listening" exercise in adjectives, so you can't get it wrong as long as you spell it right. But here in "discussion" we are given the translation which is wrong for the adjective.