What I'm thinking of is a central government that is divided into partitions, each partition designated to govern over a given field (topic, subject), and each partition having elected representatives and heads.
For example, take the United States and make the partition be roughly the federal executive departments that have a Cabinet member--so you'd have Defense, Commerce, Agriculture, Energy, Education, etc. You'd have a branch of the government in charge of defense with elected representatives and an elected head who all are to focus only on defense and the same would go for all of the branches.
With that general structure, I'm sure there would need to be mechanisms in place to ensure fluid and fair interactions on policy and implementation between and among the branches and some kind of checks and balances. But ignoring that for now, is there a term for this type of government and has anything similar to it been tried before?