Possible American Tricameral Legislature

So I posted an Ameriwank Constitution thread a week or two ago. But after posting I had an idea for a tricameral legislature for the US and was wondering about its plausibility. Specifically, I was looking at it and its potential make up. The idea I came up with was essentially similar to OTL with these changes.
  • House of Representatives - To each individual state based upon population, elected by the populace. 2 year term
  • Senate - To each state an equal number, appointed by the state. 10 year term.
  • Assembly of Chieftains - To each tribe bound in perpetual treaty to service of and protection by the United States, one Assemblyman, selected by the tribe through methods of personal selection, to a life term, to be removed from office only through election of retirement, death, or peaceable request from the tribes.
Basically, the Assembly serves as a way for tribes who have signed treaties with the United States and are a part of the Reservation System, to have direct federal representation and powers. However, I am unclear as to which powers can be derived to them specifically and exclusively.

I know that historically, tricameral legislatures served to reduce the powers of the native populace (looking at you South Africa) and I'm looking to reverse that and to provide the Amerindians more power within the US. Any ideas are welcome.
 
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