Without spoiling anything, does Adventure Time develop an overarching plot?

My son and I are only midway through season two and really enjoying it. There are lots of places where we’ve speculated on characters and possible plots, but we're extremely spoiler-averse so don't want to looking up anything about the show until we’ve finished our first wach-through.

Without spoilers, can you help us set expectations so we can either watch the show for what it is without wondering if/when an overarching plot will develop or look forward to another layer of the show?