Anyone wanna help me brainstorm special powers for my “tricameral” legislature?

There’s this one country that has a legislature that’s divided into three houses. The first is the house of provincial delegates, the second is the house of regional delegates, and the third is the house of territorial delegates.

I want to assign special roles to these three houses, but I’m having trouble coming up with anything. Any help?

So are these chambers on equal footing with each other, or is there a hierarchy?

They’re more or less on equal footing. The only difference is that the provincial delegates can convene the council for national legislation, while the regional and territorial delegates cannot.

Right! And when you say special powers, do you mean along the lines of "each chamber is the only one that can pass a specific type of legislation" or more along the lines of "this chamber has the power of veto and this chamber does research and this chamber makes the laws the others veto and research"?

The latter

Right! So I guess a good question to start out with is what sort of powers the legislature would need in order to function - so for example, they'd need people who are experts on the issues at hand and they'd need people who represent those being governed (in a democratic system, at least).
It'd also be important to ask who they'd appoint as delegates for each chamber. For example, in the UK you have the elected house of Commons and the appointed house of Lords, which necessarily means the house of Commons ends up having a more important role than the house of Lords in today's modern society since people feel those delegates have more accountability.
(I'm sorry this is all pretty vague, but I feel like the issues going on in your country would shape the way it's being governed. The special powers should definitely be tailored either to what the country needs, or what the country needed in the past, or what the country thought it needed in the past.)