Well, for example, would the various "cabinets" be defined in the Constitution? Wouldn't that be not adaptable enough? How would the executive branch be appointed? A minister per "cabinet"? Also, wouldn't it make more sense to keep a parliament, but give voters a say in who gets to seat on which committee?
Well, I rather thought about cabinets being defined by an act of lower level than Constitution (like most laws set by current parliaments) - let's call it bill, as Wikipedia seems to suggest it as a general term. Vactio legis would be long, though: new cabinet would be elected during next elections, to avoid additional elections mid-term. Those could also be removed/merged. We could even add additional question during elections with new cabinet: 'do you want this new cabinet to exist'? You know, merge referendum with vote, and not create this new cabinet if popular vote says it is useless. This isn't perhaps the most flexible approach, but I think flexibility isn't the most important part here.
Executive branch could be detached from cabinets, where necessary (for example, to allow more fine-grained control of executive branch, as flexibility here is more important, I believe). But the ministries (is it the right word for the whole office of a minister?) should be small and efficient.
Keeping the parliament and giving voters say in who gets a seat where might work, too. But it strongly depends on how much power committees have, because in Poland they seem to be rather non-important, really. The trick being you can change the law after it went through a committee if you have majority in the parliament, so it ends up shaped like the ruling party wants anyway, no matter what happens in the committees.
The problem with specialized parliaments is delimitation of power as Sheb mentioned. Who distributes issues to parliaments and what if they cannot agree on which parliament should vote for issue?
In my opinion parliaments in classic parliamentary systems are nothing but a rubber stamps for ruling party policies. If some party has over 50% of MPs, they can do anything they want and no one can really stop them. On the other hand if there are many small parties, they cannot pass anything in parliament if the big party says no.
Yep, distribution could be an issue here, that's true. That's why I propose the 'Elders Cabinet', with most-voted person from each cabinet getting a seat there, to decide which issue/bill goes where; this 'Elders Cabinet' could be created in different ways, depending on the country. For example, I would imagine King/Queen having something to say in that matter in constitutional monarchies. Or it could just be voted for normally, like the other cabinets? Maybe with some kind of limitation: only people who served at least one full term in some other cabinet can be candidates to 'Elders Cabinet'?
And the parliament being rubber stamp for ruling party is exactly the problem I would like to solve.