Puzzle Pirates is the iconic version of this for me. There's individual puzzles for low-level tasks. But these fit together to provide fodder for the higher-level games of trade, shopkeeping, sea battles, flotillas, and even dress-up. It succeeded at making the minigames both interesting and "matter".
Plenty of games have a PvE grind follwed by PvP endgame (or PvE resource-gathering for PvP battles) but these don't really feel like the same sort of thing. KadoKado offers access to new games in exchange for coins earned in other games, but I wouldn't call that a "game" at the upper level. In college we joked about having a game where you could play at the SimCity, the Civ, or the Master of Orion level of the same universe, with benefits flowing in both directions--- so Spore offers something like that but the levels are spread across time. Deck-construction games come close, particularly when success in the lower game expands your deck.
What other examples of multi-level games can you provide? (And are any of them worth playing?)